diff --git a/CMakeLists.txt b/CMakeLists.txt
index f3cb0eed4..d35172c96 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -104,6 +104,19 @@ if(NOT NOFORTRAN)
   endif()
 endif()
 
+if (NOT NOFORTRAN AND CMAKE_Fortran_COMPILER_ID STREQUAL "LLVMFlang")
+  if (CMAKE_Fortran_COMPILER_VERSION VERSION_LESS 17 OR WIN32)
+    # The *blas3 tests fail on hardware with AVX512 instruction when using
+    # LLVM Flang before version 17 or when using LLVM Flang on Windows.
+    # Tested with LLVM Flang 16 and LLVM Flang 17 on Windows (MSYS2/CLANG64).
+    # FIXME: Revisit with LLVM Flang 18.
+    if (NOT NO_AVX512)
+      message(STATUS "Disabling AVX512 instructions for LLVM Flang before version 17 or on Windows.")
+    endif()
+    set(NO_AVX512 1)
+  endif()
+endif()
+
 include("${PROJECT_SOURCE_DIR}/cmake/utils.cmake")
 include("${PROJECT_SOURCE_DIR}/cmake/system.cmake")