diff --git a/Doc/library/hashlib.rst b/Doc/library/hashlib.rst
index ed0b0b2735b5c3..5b666c5adac645 100644
--- a/Doc/library/hashlib.rst
+++ b/Doc/library/hashlib.rst
@@ -50,12 +50,15 @@ hash supplied more than 2047 bytes of data at once in its constructor or
 .. index:: single: OpenSSL; (use in module hashlib)
 
 Constructors for hash algorithms that are always present in this module are
-:func:`sha1`, :func:`sha224`, :func:`sha256`, :func:`sha384`, :func:`sha512`,
-:func:`sha3_224`, :func:`sha3_256`, :func:`sha3_384`, :func:`sha3_512`,
-:func:`shake_128`, :func:`shake_256`, :func:`blake2b`, and :func:`blake2s`.
-:func:`md5` is normally available as well, though it may be missing or blocked
-if you are using a rare "FIPS compliant" build of Python.
-These correspond to :data:`algorithms_guaranteed`.
+:func:`md5`, :func:`sha1`, :func:`sha224`, :func:`sha256`, :func:`sha384`,
+:func:`sha512`, :func:`sha3_224`, :func:`sha3_256`, :func:`sha3_384`,
+:func:`sha3_512`, :func:`shake_128`, :func:`shake_256`, :func:`blake2b`, and
+:func:`blake2s`.  These correspond to :data:`algorithms_guaranteed`.
+
+Any of these may nonetheless be missing or blocked in unusual environments,
+such as a rare "FIPS compliant" build of Python or when OpenSSL's "FIPS mode"
+is configured to exclude some algorithms from its default provider.  Calling
+the constructor of an algorithm that is unavailable raises :exc:`ValueError`.
 
 Additional algorithms may also be available if your Python distribution's
 :mod:`!hashlib` was linked against a build of OpenSSL that provides others.
diff --git a/Lib/hashlib.py b/Lib/hashlib.py
index 6c73eb9f31f8e4..c1e2d07c4357ff 100644
--- a/Lib/hashlib.py
+++ b/Lib/hashlib.py
@@ -261,16 +261,15 @@ def file_digest(fileobj, digest, /, *, _bufsize=2**18):
     return digestobj
 
 
-__logging = None
 for __func_name in __always_supported:
     # try them all, some may not work due to the OpenSSL
     # version not supporting that algorithm.
     try:
         globals()[__func_name] = __get_hash(__func_name)
-    except ValueError as __exc:
-        import logging as __logging
-        __logging.error('hash algorithm %s will not be supported at runtime '
-                        '[reason: %s]', __func_name, __exc)
+    except ValueError:
+        # Don't log here: logging at import time has global side effects and
+        # would tell the wrong audience; code that uses a missing algorithm
+        # gets a ValueError from the stub installed below.
         # The following code can be simplified in Python 3.19
         # once "string" is removed from the signature.
         __code = f'''\
@@ -291,9 +290,8 @@ def {__func_name}(data=__UNSET, *, usedforsecurity=True, string=__UNSET):
 '''
         exec(__code, {"__UNSET": object()}, __locals := {})
         globals()[__func_name] = __locals[__func_name]
-        del __exc, __code, __locals
+        del __code, __locals
 
 # Cleanup locals()
 del __always_supported, __func_name, __get_hash
 del __py_new, __hash_new, __get_openssl_constructor
-del __logging
diff --git a/Misc/NEWS.d/next/Library/2026-06-29-01-08-53.gh-issue-110357.QGWdZQ.rst b/Misc/NEWS.d/next/Library/2026-06-29-01-08-53.gh-issue-110357.QGWdZQ.rst
new file mode 100644
index 00000000000000..7c2384ea76fe53
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2026-06-29-01-08-53.gh-issue-110357.QGWdZQ.rst
@@ -0,0 +1,6 @@
+Importing :mod:`hashlib` no longer logs an error to stderr when a normally
+guaranteed hash algorithm is unavailable in the current runtime (for example
+under an OpenSSL FIPS configuration or a build using
+:option:`--without-builtin-hashlib-hashes <--with-builtin-hashlib-hashes>`).
+Code that actually uses the missing algorithm still gets a clear
+:exc:`ValueError`.