diff --git a/Misc/NEWS.d/next/Library/2019-09-14-10-34-00.bpo-33936.8wCI_n.rst b/Misc/NEWS.d/next/Library/2019-09-14-10-34-00.bpo-33936.8wCI_n.rst
new file mode 100644
index 00000000000..7bc7fed483a
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2019-09-14-10-34-00.bpo-33936.8wCI_n.rst
@@ -0,0 +1,2 @@
+_hashlib no longer calls obsolete OpenSSL initialization function with
+OpenSSL 1.1.0+.
diff --git a/Modules/_hashopenssl.c b/Modules/_hashopenssl.c
index b86cbd09743..d963c7a5722 100644
--- a/Modules/_hashopenssl.c
+++ b/Modules/_hashopenssl.c
@@ -1138,7 +1138,7 @@ PyInit__hashlib(void)
 {
     PyObject *m, *openssl_md_meth_names;
 
-#ifndef OPENSSL_VERSION_1_1
+#if (OPENSSL_VERSION_NUMBER < 0x10100000L) || defined(LIBRESSL_VERSION_NUMBER)
     /* Load all digest algorithms and initialize cpuid */
     OPENSSL_add_all_algorithms_noconf();
     ERR_load_crypto_strings();