diff --git a/clang-tools-extra/clangd/IncludeCleaner.cpp b/clang-tools-extra/clangd/IncludeCleaner.cpp
--- a/clang-tools-extra/clangd/IncludeCleaner.cpp
+++ b/clang-tools-extra/clangd/IncludeCleaner.cpp
@@ -255,6 +255,12 @@
           ->getName()
           .str();
   for (const auto *Inc : computeUnusedIncludes(AST)) {
+    // FIXME(kirillbobyrev): Standard library headers are not handled correctly
+    // now because the symbols are typically not directly defined in the
+    // available headers. Suppress the warnings from any headers enclosed in
+    // angle brackets until we fully support the Standard Library features.
+    if (Inc->Written.front() == '<')
+      continue;
     Diag D;
     D.Message =
         llvm::formatv("included header {0} is not used",
diff --git a/clang-tools-extra/clangd/unittests/DiagnosticsTests.cpp b/clang-tools-extra/clangd/unittests/DiagnosticsTests.cpp
--- a/clang-tools-extra/clangd/unittests/DiagnosticsTests.cpp
+++ b/clang-tools-extra/clangd/unittests/DiagnosticsTests.cpp
@@ -1483,7 +1483,9 @@
 TEST(DiagnosticsTest, IncludeCleaner) {
   Annotations Test(R"cpp(
 $fix[[  $diag[[#include "unused.h"]]
-]]  #include "used.h"
+]]#include "used.h"
+
+  #include <system_header.h>
 
   void foo() {
     used();
@@ -1497,6 +1499,8 @@
   TU.AdditionalFiles["used.h"] = R"cpp(
     void used() {}
   )cpp";
+  TU.AdditionalFiles["system/system_header.h"] = "";
+  TU.ExtraArgs = {"-isystem" + testPath("system")};
   // Off by default.
   EXPECT_THAT(*TU.build().getDiagnostics(), IsEmpty());
   Config Cfg;
diff --git a/clang-tools-extra/clangd/unittests/IncludeCleanerTests.cpp b/clang-tools-extra/clangd/unittests/IncludeCleanerTests.cpp
--- a/clang-tools-extra/clangd/unittests/IncludeCleanerTests.cpp
+++ b/clang-tools-extra/clangd/unittests/IncludeCleanerTests.cpp
@@ -177,6 +177,7 @@
     #include "dir/c.h"
     #include "dir/unused.h"
     #include "unused.h"
+    #include <system_header.h>
     void foo() {
       a();
       b();
@@ -191,17 +192,17 @@
   TU.AdditionalFiles["dir/c.h"] = "void c();";
   TU.AdditionalFiles["unused.h"] = "void unused();";
   TU.AdditionalFiles["dir/unused.h"] = "void dirUnused();";
-  TU.AdditionalFiles["not_included.h"] = "void notIncluded();";
-  TU.ExtraArgs = {"-I" + testPath("dir")};
+  TU.AdditionalFiles["system/system_header.h"] = "";
+  TU.ExtraArgs.push_back("-I" + testPath("dir"));
+  TU.ExtraArgs.push_back("-isystem" + testPath("system"));
   TU.Code = MainFile.str();
   ParsedAST AST = TU.build();
-  auto UnusedIncludes = computeUnusedIncludes(AST);
-  std::vector<std::string> UnusedHeaders;
-  UnusedHeaders.reserve(UnusedIncludes.size());
-  for (const auto &Include : UnusedIncludes)
-    UnusedHeaders.push_back(Include->Written);
-  EXPECT_THAT(UnusedHeaders,
-              UnorderedElementsAre("\"unused.h\"", "\"dir/unused.h\""));
+  std::vector<std::string> UnusedIncludes;
+  for (const auto &Include : computeUnusedIncludes(AST))
+    UnusedIncludes.push_back(Include->Written);
+  EXPECT_THAT(UnusedIncludes,
+              UnorderedElementsAre("\"unused.h\"", "\"dir/unused.h\"",
+                                   "<system_header.h>"));
 }
 
 TEST(IncludeCleaner, ScratchBuffer) {