diff --git a/Doc/library/ssl.rst b/Doc/library/ssl.rst
index 3cd9554c081..9b3306cdd14 100644
--- a/Doc/library/ssl.rst
+++ b/Doc/library/ssl.rst
@@ -445,6 +445,14 @@ Constants
 
    .. versionadded:: 3.3
 
+.. data:: HAS_ECDH
+
+   Whether the OpenSSL library has built-in support for Elliptic Curve-based
+   Diffie-Hellman key exchange.  This should be true unless the feature was
+   explicitly disabled by the distributor.
+
+   .. versionadded:: 3.3
+
 .. data:: HAS_SNI
 
    Whether the OpenSSL library has built-in support for the *Server Name
@@ -711,6 +719,8 @@ to speed up repeated connections from the same clients.
    This setting doesn't apply to client sockets.  You can also use the
    :data:`OP_SINGLE_ECDH_USE` option to further improve security.
 
+   This method is not available if :data:`HAS_ECDH` is False.
+
    .. versionadded:: 3.3
 
    .. seealso::
diff --git a/Lib/ssl.py b/Lib/ssl.py
index 0b2f743f227..d43d25512ef 100644
--- a/Lib/ssl.py
+++ b/Lib/ssl.py
@@ -86,7 +86,7 @@ from _ssl import (
     SSL_ERROR_EOF,
     SSL_ERROR_INVALID_ERROR_CODE,
     )
-from _ssl import HAS_SNI
+from _ssl import HAS_SNI, HAS_ECDH
 from _ssl import (PROTOCOL_SSLv3, PROTOCOL_SSLv23,
                   PROTOCOL_TLSv1)
 from _ssl import _OPENSSL_API_VERSION
diff --git a/Lib/test/test_ssl.py b/Lib/test/test_ssl.py
index 8bbe0f77fe2..1960e143473 100644
--- a/Lib/test/test_ssl.py
+++ b/Lib/test/test_ssl.py
@@ -103,6 +103,7 @@ class BasicSocketTests(unittest.TestCase):
         if ssl.OPENSSL_VERSION_INFO >= (1, 0):
             ssl.OP_NO_COMPRESSION
         self.assertIn(ssl.HAS_SNI, {True, False})
+        self.assertIn(ssl.HAS_ECDH, {True, False})
 
     def test_random(self):
         v = ssl.RAND_status()
@@ -561,6 +562,7 @@ class ContextTests(unittest.TestCase):
         ctx = ssl.SSLContext(ssl.PROTOCOL_TLSv1)
         ctx.set_default_verify_paths()
 
+    @unittest.skipUnless(ssl.HAS_ECDH, "ECDH disabled on this OpenSSL build")
     def test_set_ecdh_curve(self):
         ctx = ssl.SSLContext(ssl.PROTOCOL_TLSv1)
         ctx.set_ecdh_curve("prime256v1")
diff --git a/Modules/_ssl.c b/Modules/_ssl.c
index 480543cbe16..02fe5f356ec 100644
--- a/Modules/_ssl.c
+++ b/Modules/_ssl.c
@@ -2006,6 +2006,7 @@ set_default_verify_paths(PySSLContext *self, PyObject *unused)
     Py_RETURN_NONE;
 }
 
+#ifndef OPENSSL_NO_ECDH
 static PyObject *
 set_ecdh_curve(PySSLContext *self, PyObject *name)
 {
@@ -2032,6 +2033,7 @@ set_ecdh_curve(PySSLContext *self, PyObject *name)
     EC_KEY_free(key);
     Py_RETURN_NONE;
 }
+#endif
 
 static PyGetSetDef context_getsetlist[] = {
     {"options", (getter) get_options,
@@ -2054,8 +2056,10 @@ static struct PyMethodDef context_methods[] = {
                       METH_NOARGS, NULL},
     {"set_default_verify_paths", (PyCFunction) set_default_verify_paths,
                                  METH_NOARGS, NULL},
+#ifndef OPENSSL_NO_ECDH
     {"set_ecdh_curve", (PyCFunction) set_ecdh_curve,
                        METH_O, NULL},
+#endif
     {NULL, NULL}        /* sentinel */
 };
 
@@ -2523,6 +2527,14 @@ PyInit__ssl(void)
     Py_INCREF(r);
     PyModule_AddObject(m, "HAS_TLS_UNIQUE", r);
 
+#ifdef OPENSSL_NO_ECDH
+    r = Py_False;
+#else
+    r = Py_True;
+#endif
+    Py_INCREF(r);
+    PyModule_AddObject(m, "HAS_ECDH", r);
+
     /* OpenSSL version */
     /* SSLeay() gives us the version of the library linked against,
        which could be different from the headers version.