diff --git a/Source/cmGeneratorTarget.cxx b/Source/cmGeneratorTarget.cxx
index ab6a26c974..b7bf4a6f7e 100644
--- a/Source/cmGeneratorTarget.cxx
+++ b/Source/cmGeneratorTarget.cxx
@@ -6914,6 +6914,14 @@ void cmGeneratorTarget::GetLanguages(std::set<std::string>& languages,
   }
 }
 
+bool cmGeneratorTarget::IsLanguageUsed(std::string const& language,
+                                       std::string const& config) const
+{
+  std::set<std::string> languages;
+  this->GetLanguages(languages, config);
+  return languages.count(language);
+}
+
 bool cmGeneratorTarget::IsCSharpOnly() const
 {
   // Only certain target types may compile CSharp.
diff --git a/Source/cmGeneratorTarget.h b/Source/cmGeneratorTarget.h
index 3aedbf53e6..ea3a684a13 100644
--- a/Source/cmGeneratorTarget.h
+++ b/Source/cmGeneratorTarget.h
@@ -397,6 +397,8 @@ public:
   // until we have per-target object file properties.
   void GetLanguages(std::set<std::string>& languages,
                     std::string const& config) const;
+  bool IsLanguageUsed(std::string const& language,
+                      std::string const& config) const;
 
   bool IsCSharpOnly() const;
 
diff --git a/Source/cmVisualStudio10TargetGenerator.cxx b/Source/cmVisualStudio10TargetGenerator.cxx
index f58c6fd717..2ea28393e2 100644
--- a/Source/cmVisualStudio10TargetGenerator.cxx
+++ b/Source/cmVisualStudio10TargetGenerator.cxx
@@ -3018,7 +3018,8 @@ bool cmVisualStudio10TargetGenerator::ComputeCudaOptions()
     return true;
   }
   for (std::string const& c : this->Configurations) {
-    if (!this->ComputeCudaOptions(c)) {
+    if (this->GeneratorTarget->IsLanguageUsed("CUDA", c) &&
+        !this->ComputeCudaOptions(c)) {
       return false;
     }
   }
@@ -3158,7 +3159,8 @@ bool cmVisualStudio10TargetGenerator::ComputeCudaOptions(
 void cmVisualStudio10TargetGenerator::WriteCudaOptions(
   Elem& e1, std::string const& configName)
 {
-  if (!this->MSTools || !this->GlobalGenerator->IsCudaEnabled()) {
+  if (!this->MSTools || !this->GlobalGenerator->IsCudaEnabled() ||
+      !this->GeneratorTarget->IsLanguageUsed("CUDA", configName)) {
     return;
   }
   Elem e2(e1, "CudaCompile");
diff --git a/Tests/RunCMake/CMP0104/CMP0104-Common.cmake b/Tests/RunCMake/CMP0104/CMP0104-Common.cmake
index b3568f113d..ca4c1aa225 100644
--- a/Tests/RunCMake/CMP0104/CMP0104-Common.cmake
+++ b/Tests/RunCMake/CMP0104/CMP0104-Common.cmake
@@ -1,2 +1,6 @@
+# Make sure CMP0104 isn't issued for CXX targets created prior to enabling CUDA. See #21341.
+enable_language(CXX)
+add_library(cxx main.cxx)
+
 enable_language(CUDA)
 add_library(cuda main.cu)
diff --git a/Tests/RunCMake/CMP0104/main.cxx b/Tests/RunCMake/CMP0104/main.cxx
new file mode 100644
index 0000000000..5047a34e39
--- /dev/null
+++ b/Tests/RunCMake/CMP0104/main.cxx
@@ -0,0 +1,3 @@
+int main()
+{
+}