diff --git a/Sources/SemanticIndex/SemanticIndexManager.swift b/Sources/SemanticIndex/SemanticIndexManager.swift
index d719e0d71..00f3f5265 100644
--- a/Sources/SemanticIndex/SemanticIndexManager.swift
+++ b/Sources/SemanticIndex/SemanticIndexManager.swift
@@ -455,10 +455,19 @@ public final actor SemanticIndexManager {
     // schedule two indexing jobs for the same file in quick succession, only the first one actually updates the index
     // store and the second one will be a no-op once it runs.
     let outOfDateFiles = await filesToIndex(toCover: files).asyncFilter {
-      return await !indexStoreUpToDateStatus.isUpToDate($0.sourceFile)
+      if await indexStoreUpToDateStatus.isUpToDate($0.sourceFile) {
+        return false
+      }
+      guard let language = await buildSystemManager.defaultLanguage(for: $0.mainFile),
+        UpdateIndexStoreTaskDescription.canIndex(language: language)
+      else {
+        return false
+      }
+      return true
     }
     // sort files to get deterministic indexing order
     .sorted(by: { $0.sourceFile.stringValue < $1.sourceFile.stringValue })
+    logger.debug("Scheduling indexing of \(outOfDateFiles.map(\.sourceFile.stringValue).joined(separator: ", "))")
 
     // Sort the targets in topological order so that low-level targets get built before high-level targets, allowing us
     // to index the low-level targets ASAP.
diff --git a/Sources/SemanticIndex/UpdateIndexStoreTaskDescription.swift b/Sources/SemanticIndex/UpdateIndexStoreTaskDescription.swift
index 3183b84ca..3d856628b 100644
--- a/Sources/SemanticIndex/UpdateIndexStoreTaskDescription.swift
+++ b/Sources/SemanticIndex/UpdateIndexStoreTaskDescription.swift
@@ -76,6 +76,22 @@ public struct FileAndTarget: Sendable {
   public let target: ConfiguredTarget
 }
 
+private enum IndexKind {
+  case clang
+  case swift
+
+  init?(language: Language) {
+    switch language {
+    case .swift:
+      self = .swift
+    case .c, .cpp, .objective_c, .objective_cpp:
+      self = .clang
+    default:
+      return nil
+    }
+  }
+}
+
 /// Describes a task to index a set of source files.
 ///
 /// This task description can be scheduled in a `TaskScheduler`.
@@ -114,6 +130,10 @@ public struct UpdateIndexStoreTaskDescription: IndexTaskDescription {
     return "update-indexstore-\(id)"
   }
 
+  static func canIndex(language: Language) -> Bool {
+    return IndexKind(language: language) != nil
+  }
+
   init(
     filesToIndex: [FileAndTarget],
     buildSystemManager: BuildSystemManager,
@@ -219,7 +239,7 @@ public struct UpdateIndexStoreTaskDescription: IndexTaskDescription {
       return
     }
     let startDate = Date()
-    switch language {
+    switch IndexKind(language: language) {
     case .swift:
       do {
         try await updateIndexStore(
@@ -231,7 +251,7 @@ public struct UpdateIndexStoreTaskDescription: IndexTaskDescription {
         logger.error("Updating index store for \(file.forLogging) failed: \(error.forLogging)")
         BuildSettingsLogger.log(settings: buildSettings, for: file.mainFile)
       }
-    case .c, .cpp, .objective_c, .objective_cpp:
+    case .clang:
       do {
         try await updateIndexStore(
           forClangFile: file.mainFile,
@@ -242,7 +262,7 @@ public struct UpdateIndexStoreTaskDescription: IndexTaskDescription {
         logger.error("Updating index store for \(file) failed: \(error.forLogging)")
         BuildSettingsLogger.log(settings: buildSettings, for: file.mainFile)
       }
-    default:
+    case nil:
       logger.error(
         "Not updating index store for \(file) because it is a language that is not supported by background indexing"
       )
diff --git a/Tests/SourceKitLSPTests/BackgroundIndexingTests.swift b/Tests/SourceKitLSPTests/BackgroundIndexingTests.swift
index 9c306db27..9797bb745 100644
--- a/Tests/SourceKitLSPTests/BackgroundIndexingTests.swift
+++ b/Tests/SourceKitLSPTests/BackgroundIndexingTests.swift
@@ -740,4 +740,51 @@ final class BackgroundIndexingTests: XCTestCase {
       cleanUp: { expectedIndexTaskTracker.keepAlive() }
     )
   }
+
+  func testNoIndexingHappensWhenPackageIsReopened() async throws {
+    let project = try await SwiftPMTestProject(
+      files: [
+        "SwiftLib/NonEmptySwiftFile.swift": """
+        func test() {}
+        """,
+        "CLib/include/EmptyHeader.h": "",
+        "CLib/Assembly.S": "",
+        "CLib/EmptyC.c": "",
+        "CLib/NonEmptyC.c": """
+        void test() {}
+        """,
+      ],
+      manifest: """
+        // swift-tools-version: 5.7
+
+        import PackageDescription
+
+        let package = Package(
+          name: "MyLibrary",
+          targets: [
+            .target(name: "SwiftLib"),
+            .target(name: "CLib"),
+          ]
+        )
+        """,
+      serverOptions: backgroundIndexingOptions
+    )
+
+    var otherClientOptions = backgroundIndexingOptions
+    otherClientOptions.indexTestHooks = IndexTestHooks(
+      preparationTaskDidStart: { taskDescription in
+        XCTFail("Did not expect any target preparation, got \(taskDescription.targetsToPrepare)")
+      },
+      updateIndexStoreTaskDidStart: { taskDescription in
+        XCTFail("Did not expect any indexing tasks, got \(taskDescription.filesToIndex)")
+      }
+    )
+    let otherClient = try await TestSourceKitLSPClient(
+      serverOptions: otherClientOptions,
+      workspaceFolders: [
+        WorkspaceFolder(uri: DocumentURI(project.scratchDirectory))
+      ]
+    )
+    _ = try await otherClient.send(PollIndexRequest())
+  }
 }