diff --git a/clang/CMakeLists.txt b/clang/CMakeLists.txt
--- a/clang/CMakeLists.txt
+++ b/clang/CMakeLists.txt
@@ -131,7 +131,8 @@
   set( CMAKE_ARCHIVE_OUTPUT_DIRECTORY ${CMAKE_BINARY_DIR}/lib${LLVM_LIBDIR_SUFFIX} )
 
   if(LLVM_INCLUDE_TESTS)
-    find_package(Python3 REQUIRED COMPONENTS Interpreter)
+    find_package(Python3 ${LLVM_MINIMUM_PYTHON_VERSION} REQUIRED
+      COMPONENTS Interpreter)
 
     # Check prebuilt llvm/utils.
     if(EXISTS ${LLVM_TOOLS_BINARY_DIR}/FileCheck${CMAKE_EXECUTABLE_SUFFIX}
diff --git a/lld/CMakeLists.txt b/lld/CMakeLists.txt
--- a/lld/CMakeLists.txt
+++ b/lld/CMakeLists.txt
@@ -57,7 +57,8 @@
   include(CheckAtomic)
 
   if(LLVM_INCLUDE_TESTS)
-    find_package(Python3 REQUIRED COMPONENTS Interpreter)
+    find_package(Python3 ${LLVM_MINIMUM_PYTHON_VERSION} REQUIRED
+      COMPONENTS Interpreter)
 
     # Check prebuilt llvm/utils.
     if(EXISTS ${LLVM_TOOLS_BINARY_DIR}/FileCheck${CMAKE_EXECUTABLE_SUFFIX}
diff --git a/llvm/CMakeLists.txt b/llvm/CMakeLists.txt
--- a/llvm/CMakeLists.txt
+++ b/llvm/CMakeLists.txt
@@ -697,7 +697,8 @@
 
 include(HandleLLVMOptions)
 
-find_package(Python3 REQUIRED COMPONENTS Interpreter)
+find_package(Python3 ${LLVM_MINIMUM_PYTHON_VERSION} REQUIRED
+    COMPONENTS Interpreter)
 
 ######
 
diff --git a/llvm/cmake/modules/HandleLLVMOptions.cmake b/llvm/cmake/modules/HandleLLVMOptions.cmake
--- a/llvm/cmake/modules/HandleLLVMOptions.cmake
+++ b/llvm/cmake/modules/HandleLLVMOptions.cmake
@@ -1147,3 +1147,11 @@
   append_if(SUPPORTS_FFILE_PREFIX_MAP "-ffile-prefix-map=${source_root}/=${LLVM_SOURCE_PREFIX}" CMAKE_C_FLAGS CMAKE_CXX_FLAGS)
   add_flag_if_supported("-no-canonical-prefixes" NO_CANONICAL_PREFIXES)
 endif()
+
+if(LLVM_INCLUDE_TESTS)
+  # Lit test suite requires at least python 3.6
+  set(LLVM_MINIMUM_PYTHON_VERSION 3.6)
+else()
+  # FIXME: it is unknown if this is the actual minimum bound
+  set(LLVM_MINIMUM_PYTHON_VERSION 3.0)
+endif()
diff --git a/mlir/CMakeLists.txt b/mlir/CMakeLists.txt
--- a/mlir/CMakeLists.txt
+++ b/mlir/CMakeLists.txt
@@ -79,7 +79,8 @@
 
 if(MLIR_BINDINGS_PYTHON_ENABLED)
   include(MLIRDetectPythonEnv)
-  find_package(Python3 COMPONENTS Interpreter Development NumPy REQUIRED)
+  find_package(Python3 ${LLVM_MINIMUM_PYTHON_VERSION}
+    COMPONENTS Interpreter Development NumPy REQUIRED)
   message(STATUS "Found python include dirs: ${Python3_INCLUDE_DIRS}")
   message(STATUS "Found python libraries: ${Python3_LIBRARIES}")
   message(STATUS "Found numpy v${Python3_NumPy_VERSION}: ${Python3_NumPy_INCLUDE_DIRS}")