diff --git a/plugin/trino-phoenix/src/main/java/io/trino/plugin/phoenix/PhoenixClient.java b/plugin/trino-phoenix/src/main/java/io/trino/plugin/phoenix/PhoenixClient.java
index 3c97310c9f7f..4f78686327a0 100644
--- a/plugin/trino-phoenix/src/main/java/io/trino/plugin/phoenix/PhoenixClient.java
+++ b/plugin/trino-phoenix/src/main/java/io/trino/plugin/phoenix/PhoenixClient.java
@@ -91,6 +91,7 @@
 import java.io.IOException;
 import java.sql.Array;
 import java.sql.Connection;
+import java.sql.DatabaseMetaData;
 import java.sql.JDBCType;
 import java.sql.PreparedStatement;
 import java.sql.ResultSet;
@@ -375,6 +376,20 @@ protected String getTableSchemaName(ResultSet resultSet)
         return firstNonNull(resultSet.getString("TABLE_SCHEM"), DEFAULT_SCHEMA);
     }
 
+    @Override
+    protected ResultSet getColumns(JdbcTableHandle handle, DatabaseMetaData metadata)
+            throws SQLException
+    {
+        try {
+            return super.getColumns(handle, metadata);
+        }
+        catch (org.apache.phoenix.schema.TableNotFoundException e) {
+            // Most JDBC driver return an empty result when DatabaseMetaData.getColumns can't find objects, but Phoenix driver throws an exception
+            // Rethrow as Trino TableNotFoundException to suppress the exception during listing information_schema
+            throw new io.trino.spi.connector.TableNotFoundException(new SchemaTableName(handle.getSchemaName(), handle.getTableName()));
+        }
+    }
+
     @Override
     public Optional<ColumnMapping> toColumnMapping(ConnectorSession session, Connection connection, JdbcTypeHandle typeHandle)
     {
diff --git a/plugin/trino-phoenix/src/test/java/io/trino/plugin/phoenix/TestPhoenixConnectorTest.java b/plugin/trino-phoenix/src/test/java/io/trino/plugin/phoenix/TestPhoenixConnectorTest.java
index 5dc2c7184dc0..8a58c68a844c 100644
--- a/plugin/trino-phoenix/src/test/java/io/trino/plugin/phoenix/TestPhoenixConnectorTest.java
+++ b/plugin/trino-phoenix/src/test/java/io/trino/plugin/phoenix/TestPhoenixConnectorTest.java
@@ -22,7 +22,6 @@
 import io.trino.testing.TestingConnectorBehavior;
 import io.trino.testing.sql.SqlExecutor;
 import io.trino.testing.sql.TestTable;
-import io.trino.testng.services.Flaky;
 import org.testng.SkipException;
 import org.testng.annotations.AfterClass;
 import org.testng.annotations.Test;
@@ -221,30 +220,6 @@ public void testShowCreateTable()
                         ")");
     }
 
-    // TODO (https://github.com/trinodb/trino/issues/10904): Test is flaky because tests execute in parallel
-    @Flaky(issue = "https://github.com/trinodb/trino/issues/10904", match = "\\QERROR 1012 (42M03): Table undefined. tableName=")
-    @Test
-    @Override
-    public void testSelectInformationSchemaColumns()
-    {
-        super.testSelectInformationSchemaColumns();
-    }
-
-    @Override
-    public void testReadMetadataWithRelationsConcurrentModifications()
-    {
-        try {
-            super.testReadMetadataWithRelationsConcurrentModifications();
-        }
-        catch (Exception expected) {
-            // The test failure is not guaranteed
-            // TODO (https://github.com/trinodb/trino/issues/10904): shouldn't fail
-            assertThat(expected)
-                    .hasMessageContaining("ERROR 1012 (42M03): Table undefined. tableName=");
-            throw new SkipException("to be fixed");
-        }
-    }
-
     @Override
     public void testCharVarcharComparison()
     {
diff --git a/plugin/trino-phoenix5/src/main/java/io/trino/plugin/phoenix5/PhoenixClient.java b/plugin/trino-phoenix5/src/main/java/io/trino/plugin/phoenix5/PhoenixClient.java
index b6ff2f589e29..fdc59d0c8d28 100644
--- a/plugin/trino-phoenix5/src/main/java/io/trino/plugin/phoenix5/PhoenixClient.java
+++ b/plugin/trino-phoenix5/src/main/java/io/trino/plugin/phoenix5/PhoenixClient.java
@@ -92,6 +92,7 @@
 import java.io.IOException;
 import java.sql.Array;
 import java.sql.Connection;
+import java.sql.DatabaseMetaData;
 import java.sql.JDBCType;
 import java.sql.PreparedStatement;
 import java.sql.ResultSet;
@@ -367,6 +368,20 @@ protected String getTableSchemaName(ResultSet resultSet)
         return firstNonNull(resultSet.getString("TABLE_SCHEM"), DEFAULT_SCHEMA);
     }
 
+    @Override
+    protected ResultSet getColumns(JdbcTableHandle handle, DatabaseMetaData metadata)
+            throws SQLException
+    {
+        try {
+            return super.getColumns(handle, metadata);
+        }
+        catch (org.apache.phoenix.schema.TableNotFoundException e) {
+            // Most JDBC driver return an empty result when DatabaseMetaData.getColumns can't find objects, but Phoenix driver throws an exception
+            // Rethrow as Trino TableNotFoundException to suppress the exception during listing information_schema
+            throw new io.trino.spi.connector.TableNotFoundException(new SchemaTableName(handle.getSchemaName(), handle.getTableName()));
+        }
+    }
+
     @Override
     public Optional<ColumnMapping> toColumnMapping(ConnectorSession session, Connection connection, JdbcTypeHandle typeHandle)
     {
diff --git a/plugin/trino-phoenix5/src/test/java/io/trino/plugin/phoenix5/TestPhoenixConnectorTest.java b/plugin/trino-phoenix5/src/test/java/io/trino/plugin/phoenix5/TestPhoenixConnectorTest.java
index 1840e546c448..1107244bff7b 100644
--- a/plugin/trino-phoenix5/src/test/java/io/trino/plugin/phoenix5/TestPhoenixConnectorTest.java
+++ b/plugin/trino-phoenix5/src/test/java/io/trino/plugin/phoenix5/TestPhoenixConnectorTest.java
@@ -24,7 +24,6 @@
 import io.trino.testing.TestingConnectorBehavior;
 import io.trino.testing.sql.SqlExecutor;
 import io.trino.testing.sql.TestTable;
-import io.trino.testng.services.Flaky;
 import org.testng.SkipException;
 import org.testng.annotations.AfterClass;
 import org.testng.annotations.Test;
@@ -239,30 +238,6 @@ public void testShowCreateTable()
                         ")");
     }
 
-    // TODO (https://github.com/trinodb/trino/issues/10904): Test is flaky because tests execute in parallel
-    @Flaky(issue = "https://github.com/trinodb/trino/issues/10904", match = "\\QERROR 1012 (42M03): Table undefined. tableName=")
-    @Test
-    @Override
-    public void testSelectInformationSchemaColumns()
-    {
-        super.testSelectInformationSchemaColumns();
-    }
-
-    @Override
-    public void testReadMetadataWithRelationsConcurrentModifications()
-    {
-        try {
-            super.testReadMetadataWithRelationsConcurrentModifications();
-        }
-        catch (Exception expected) {
-            // The test failure is not guaranteed
-            // TODO (https://github.com/trinodb/trino/issues/10904): shouldn't fail
-            assertThat(expected)
-                    .hasMessageContaining("ERROR 1012 (42M03): Table undefined. tableName=");
-            throw new SkipException("to be fixed");
-        }
-    }
-
     @Override
     public void testCharVarcharComparison()
     {