diff --git a/compiler/rustc_codegen_llvm/src/coverageinfo/mapgen.rs b/compiler/rustc_codegen_llvm/src/coverageinfo/mapgen.rs
index 39fb0aeed0714..3037672801dee 100644
--- a/compiler/rustc_codegen_llvm/src/coverageinfo/mapgen.rs
+++ b/compiler/rustc_codegen_llvm/src/coverageinfo/mapgen.rs
@@ -80,10 +80,6 @@ pub(crate) fn finalize(cx: &CodegenCx<'_, '_>) {
     let filenames_val = cx.const_bytes(&filenames_buffer);
     let filenames_ref = llvm_cov::hash_bytes(&filenames_buffer);
 
-    // Generate the coverage map header, which contains the filenames used by
-    // this CGU's coverage mappings, and store it in a well-known global.
-    generate_covmap_record(cx, covmap_version, filenames_size, filenames_val);
-
     let mut unused_function_names = Vec::new();
 
     let covfun_records = function_coverage_map
@@ -93,6 +89,12 @@ pub(crate) fn finalize(cx: &CodegenCx<'_, '_>) {
         })
         .collect::<Vec<_>>();
 
+    // If there are no covfun records for this CGU, don't generate a covmap record.
+    // This should prevent a repeat of <https://github.com/rust-lang/rust/issues/133606>.
+    if covfun_records.is_empty() {
+        return;
+    }
+
     for covfun in &covfun_records {
         unused_function_names.extend(covfun.mangled_function_name_if_unused());
 
@@ -117,6 +119,10 @@ pub(crate) fn finalize(cx: &CodegenCx<'_, '_>) {
         llvm::set_linkage(array, llvm::Linkage::InternalLinkage);
         llvm::set_initializer(array, initializer);
     }
+
+    // Generate the coverage map header, which contains the filenames used by
+    // this CGU's coverage mappings, and store it in a well-known global.
+    generate_covmap_record(cx, covmap_version, filenames_size, filenames_val);
 }
 
 /// Maps "global" (per-CGU) file ID numbers to their underlying filenames.
diff --git a/tests/codegen/instrument-coverage/testprog.rs b/tests/codegen/instrument-coverage/testprog.rs
index 655fe779fca6c..aec526122b8e0 100644
--- a/tests/codegen/instrument-coverage/testprog.rs
+++ b/tests/codegen/instrument-coverage/testprog.rs
@@ -73,12 +73,12 @@ fn main() {
 
 // WIN:          $__llvm_profile_runtime_user = comdat any
 
-// CHECK:        @__llvm_coverage_mapping = private constant
-// CHECK-SAME:   section "[[INSTR_PROF_COVMAP]]", align 8
-
 // CHECK:        @__covrec_{{[A-F0-9]+}}u = linkonce_odr hidden constant
 // CHECK-SAME:   section "[[INSTR_PROF_COVFUN]]"[[COMDAT_IF_SUPPORTED]], align 8
 
+// CHECK:        @__llvm_coverage_mapping = private constant
+// CHECK-SAME:   section "[[INSTR_PROF_COVMAP]]", align 8
+
 // WIN:          @__llvm_profile_runtime = external{{.*}}global i32
 
 // CHECK:        @__profc__R{{[a-zA-Z0-9_]+}}testprog14will_be_called = {{private|internal}} global