diff --git a/.github/workflows/build.yml b/.github/workflows/build.yml
index eb050caab..9942a6fba 100644
--- a/.github/workflows/build.yml
+++ b/.github/workflows/build.yml
@@ -89,7 +89,7 @@ jobs:
     - name: "(vcpkg only) install setuptools"
       if: ${{ matrix.package_manager == 'vcpkg' }}
       run: |
-        pip install setuptools
+        pip install setuptools wheel
 
     - name: Configure CMake
       run: >
diff --git a/cmake/MakePythonWheel.cmake b/cmake/MakePythonWheel.cmake
index 8fddd0758..226098796 100644
--- a/cmake/MakePythonWheel.cmake
+++ b/cmake/MakePythonWheel.cmake
@@ -26,6 +26,23 @@ except ImportError as e:
         message(FATAL_ERROR "Python module `setuptools` required for correct wheel filename generation.")
     endif()
 
+    execute_process(
+        COMMAND ${Python3_EXECUTABLE} -c "
+import sys
+try:
+    from wheel.bdist_wheel import bdist_wheel
+    sys.exit(0)
+except ImportError as e:
+    print(f'{e}. Search paths:', file=sys.stderr)
+    for p in sys.path: print(f'  {p}', file=sys.stderr)
+    sys.exit(1)
+"
+    RESULT_VARIABLE has_bdist_wheel)
+
+    if(has_bdist_wheel EQUAL "1")
+        message(FATAL_ERROR "Python module `wheel.bdist_wheel` required for correct wheel filename generation.")
+    endif()
+
     execute_process(
         COMMAND ${Python3_EXECUTABLE} -c "
 from setuptools.dist import Distribution
@@ -46,9 +63,13 @@ print(wheel_name(name='${python_module}', version='${version}', ext_modules=[Ext
 "
         OUTPUT_VARIABLE wheel_filename
         OUTPUT_STRIP_TRAILING_WHITESPACE
-        ERROR_QUIET
+        RESULT_VARIABLE has_wheel_filename
     )
 
+    if(NOT has_wheel_filename EQUAL "0")
+        message(FATAL_ERROR "Cannot format wheel filename via 'setuptools'.")
+    endif()
+
     set(wheel_filename "${CMAKE_BINARY_DIR}/${wheel_filename}.whl")
     set(wheel_distinfo "${CMAKE_BINARY_DIR}/${python_module}-${version}.dist-info")
     set(wheel_data "${CMAKE_BINARY_DIR}/${python_module}-${version}.data")