diff --git a/x-pack/plugin/prometheus/src/javaRestTest/java/org/elasticsearch/xpack/prometheus/PrometheusRemoteWriteRestIT.java b/x-pack/plugin/prometheus/src/javaRestTest/java/org/elasticsearch/xpack/prometheus/PrometheusRemoteWriteRestIT.java
index 203aa2a04bd8f..e7b160e831b0e 100644
--- a/x-pack/plugin/prometheus/src/javaRestTest/java/org/elasticsearch/xpack/prometheus/PrometheusRemoteWriteRestIT.java
+++ b/x-pack/plugin/prometheus/src/javaRestTest/java/org/elasticsearch/xpack/prometheus/PrometheusRemoteWriteRestIT.java
@@ -142,6 +142,43 @@ public void testRemoteWriteWithMultipleTimeseriesAndSamples() throws Exception {
         assertThat(new ObjectPath(hits2.getFirst()).evaluate("metrics." + metric2), equalTo(100.0));
     }
 
+    public void testRemoteWriteDropsNaNSamples() throws Exception {
+        long timestamp = System.currentTimeMillis();
+        String metricName = "nan_metric";
+
+        RemoteWrite.WriteRequest writeRequest = RemoteWrite.WriteRequest.newBuilder()
+            .addTimeseries(timeSeries(metricName, Map.of("job", "test_job"), sample(Double.NaN, timestamp)))
+            .build();
+
+        sendAndAssertSuccess(writeRequest);
+        assertFalse("NaN-only request should not create a data stream", dataStreamExists(DEFAULT_DATA_STREAM));
+    }
+
+    public void testRemoteWriteDropsNaNButKeepsValidSamples() throws Exception {
+        long timestamp = System.currentTimeMillis();
+        String metricName = "nan_mixed_metric";
+
+        RemoteWrite.WriteRequest writeRequest = RemoteWrite.WriteRequest.newBuilder()
+            .addTimeseries(
+                timeSeries(
+                    metricName,
+                    Map.of("job", "test_job"),
+                    sample(Double.NaN, timestamp - 1000),
+                    sample(42.5, timestamp),
+                    sample(Double.POSITIVE_INFINITY, timestamp + 1000),
+                    sample(Double.NEGATIVE_INFINITY, timestamp + 2000)
+                )
+            )
+            .build();
+
+        sendAndAssertSuccess(writeRequest);
+        assertTrue("Data stream should exist for valid samples", dataStreamExists(DEFAULT_DATA_STREAM));
+
+        List<Map<String, Object>> docs = searchDocs(metricName);
+        assertThat("Only finite samples should be indexed", docs, hasSize(1));
+        assertThat(new ObjectPath(docs.getFirst()).evaluate("metrics." + metricName), equalTo(42.5));
+    }
+
     public void testRemoteWriteMissingNameLabelReturns400() throws Exception {
         long timestamp = System.currentTimeMillis();
 
@@ -288,4 +325,16 @@ private ObjectPath searchSingleDoc(String dataStream, String metricName) throws
         return new ObjectPath(docs.getFirst());
     }
 
+    private boolean dataStreamExists(String dataStream) throws IOException {
+        Request request = new Request("GET", "/_data_stream/" + dataStream);
+        try {
+            client().performRequest(request);
+            return true;
+        } catch (ResponseException e) {
+            if (e.getResponse().getStatusLine().getStatusCode() == 404) {
+                return false;
+            }
+            throw e;
+        }
+    }
 }
diff --git a/x-pack/plugin/prometheus/src/main/java/org/elasticsearch/xpack/prometheus/rest/PrometheusRemoteWriteTransportAction.java b/x-pack/plugin/prometheus/src/main/java/org/elasticsearch/xpack/prometheus/rest/PrometheusRemoteWriteTransportAction.java
index 2714f27a1328b..76754b2d47fed 100644
--- a/x-pack/plugin/prometheus/src/main/java/org/elasticsearch/xpack/prometheus/rest/PrometheusRemoteWriteTransportAction.java
+++ b/x-pack/plugin/prometheus/src/main/java/org/elasticsearch/xpack/prometheus/rest/PrometheusRemoteWriteTransportAction.java
@@ -111,14 +111,22 @@ protected void doExecute(Task task, RemoteWriteRequest request, ActionListener<R
                 }
 
                 for (Sample sample : timeSeries.getSamplesList()) {
+                    if (Double.isFinite(sample.getValue()) == false) {
+                        continue;
+                    }
                     IndexRequest indexRequest = buildIndexRequest(timeSeries, sample, metricName, request.dataset, request.namespace);
                     bulkRequestBuilder.add(indexRequest);
                 }
             }
 
             if (bulkRequestBuilder.numberOfActions() == 0) {
-                String message = buildFailureSummary(totalSamples, droppedMissingName, droppedMissingName, Map.of());
-                listener.onFailure(new ElasticsearchStatusException(message, RestStatus.BAD_REQUEST));
+                if (droppedMissingName > 0) {
+                    String message = buildFailureSummary(totalSamples, droppedMissingName, droppedMissingName, Map.of());
+                    listener.onFailure(new ElasticsearchStatusException(message, RestStatus.BAD_REQUEST));
+                } else {
+                    // All samples were non-finite (NaN/Infinity) and silently dropped — not a client error
+                    listener.onResponse(new RemoteWriteResponse());
+                }
                 return;
             }
 
diff --git a/x-pack/plugin/prometheus/src/test/java/org/elasticsearch/xpack/prometheus/rest/PrometheusRemoteWriteTransportActionTests.java b/x-pack/plugin/prometheus/src/test/java/org/elasticsearch/xpack/prometheus/rest/PrometheusRemoteWriteTransportActionTests.java
index 4ff40bed5871f..0a4c7731fe282 100644
--- a/x-pack/plugin/prometheus/src/test/java/org/elasticsearch/xpack/prometheus/rest/PrometheusRemoteWriteTransportActionTests.java
+++ b/x-pack/plugin/prometheus/src/test/java/org/elasticsearch/xpack/prometheus/rest/PrometheusRemoteWriteTransportActionTests.java
@@ -251,6 +251,43 @@ protected boolean apply(String actionName, ActionRequest actionRequest, ActionLi
         assertRegisteredIndexingPressureReleased("indexing pressure should be released when execution short-circuits");
     }
 
+    public void testStalenessMarkerIsDropped() {
+        double stalenessMarker = Double.longBitsToDouble(0x7ff0000000000002L);
+        executeRequest(createWriteRequest("stale_metric", stalenessMarker, System.currentTimeMillis()));
+        verify(client, never()).execute(any(), any(), any());
+    }
+
+    public void testNaNSamplesAreDropped() {
+        executeRequest(createWriteRequest("nan_metric", Double.NaN, System.currentTimeMillis()));
+        verify(client, never()).execute(any(), any(), any());
+    }
+
+    public void testPositiveInfinitySamplesAreDropped() {
+        executeRequest(createWriteRequest("inf_metric", Double.POSITIVE_INFINITY, System.currentTimeMillis()));
+        verify(client, never()).execute(any(), any(), any());
+    }
+
+    public void testNegativeInfinitySamplesAreDropped() {
+        executeRequest(createWriteRequest("neg_inf_metric", Double.NEGATIVE_INFINITY, System.currentTimeMillis()));
+        verify(client, never()).execute(any(), any(), any());
+    }
+
+    public void testMixedFiniteAndNonFiniteSamples() {
+        long now = System.currentTimeMillis();
+        RemoteWrite.WriteRequest writeRequest = RemoteWrite.WriteRequest.newBuilder()
+            .addTimeseries(
+                RemoteWrite.TimeSeries.newBuilder()
+                    .addLabels(RemoteWrite.Label.newBuilder().setName("__name__").setValue("mixed_metric").build())
+                    .addSamples(RemoteWrite.Sample.newBuilder().setValue(Double.NaN).setTimestamp(now - 2000).build())
+                    .addSamples(RemoteWrite.Sample.newBuilder().setValue(42.0).setTimestamp(now - 1000).build())
+                    .addSamples(RemoteWrite.Sample.newBuilder().setValue(Double.POSITIVE_INFINITY).setTimestamp(now).build())
+                    .build()
+            )
+            .build();
+
+        executeRequest(createWriteRequest(writeRequest, "generic", "default"));
+    }
+
     public void testCustomDatasetAndNamespace() {
         executeRequest(createWriteRequest("test_metric", 42.0, System.currentTimeMillis(), "myapp", "production"));
     }