diff --git a/starlette/_compat.py b/starlette/_compat.py
new file mode 100644
index 000000000..82aa72f38
--- /dev/null
+++ b/starlette/_compat.py
@@ -0,0 +1,26 @@
+import hashlib
+
+# Compat wrapper to always include the `usedforsecurity=...` parameter,
+# which is only added from Python 3.9 onwards.
+# We use this flag to indicate that we use `md5` hashes only for non-security
+# cases (our ETag checksums).
+# If we don't indicate that we're using MD5 for non-security related reasons,
+# then attempting to use this function will raise an error when used
+# environments which enable a strict "FIPs mode".
+#
+# See issue: https://github.com/encode/starlette/issues/1365
+try:
+
+    hashlib.md5(b"data", usedforsecurity=True)  # type: ignore[call-arg]
+
+    def md5_hexdigest(
+        data: bytes, *, usedforsecurity: bool = True
+    ) -> str:  # pragma: no cover
+        return hashlib.md5(  # type: ignore[call-arg]
+            data, usedforsecurity=usedforsecurity
+        ).hexdigest()
+
+except TypeError:  # pragma: no cover
+
+    def md5_hexdigest(data: bytes, *, usedforsecurity: bool = True) -> str:
+        return hashlib.md5(data).hexdigest()
diff --git a/starlette/responses.py b/starlette/responses.py
index 1f9c43a21..ffde4b97d 100644
--- a/starlette/responses.py
+++ b/starlette/responses.py
@@ -1,4 +1,3 @@
-import hashlib
 import http.cookies
 import json
 import os
@@ -12,6 +11,7 @@
 
 import anyio
 
+from starlette._compat import md5_hexdigest
 from starlette.background import BackgroundTask
 from starlette.concurrency import iterate_in_threadpool
 from starlette.datastructures import URL, MutableHeaders
@@ -287,7 +287,7 @@ def set_stat_headers(self, stat_result: os.stat_result) -> None:
         content_length = str(stat_result.st_size)
         last_modified = formatdate(stat_result.st_mtime, usegmt=True)
         etag_base = str(stat_result.st_mtime) + "-" + str(stat_result.st_size)
-        etag = hashlib.md5(etag_base.encode()).hexdigest()
+        etag = md5_hexdigest(etag_base.encode(), usedforsecurity=False)
 
         self.headers.setdefault("content-length", content_length)
         self.headers.setdefault("last-modified", last_modified)