diff --git a/distributed/security.py b/distributed/security.py
index 135d661d73a..a614239d049 100644
--- a/distributed/security.py
+++ b/distributed/security.py
@@ -1,18 +1,68 @@
+from __future__ import annotations
+
 import datetime
 import os
+import sys
 import tempfile
+import warnings
 
 try:
     import ssl
 except ImportError:
     ssl = None  # type: ignore
 
+try:
+    from ssl import OPENSSL_VERSION_INFO as _OPENSSL_VERSION_INFO
+except ImportError:
+    _OPENSSL_VERSION_INFO = (0, 0, 0, 0, 0)
+
 import dask
 from dask.widgets import get_template
 
 __all__ = ("Security",)
 
 
+if sys.version_info >= (3, 10) or _OPENSSL_VERSION_INFO >= (1, 1, 0, 7):
+    # The OP_NO_SSL* and OP_NO_TLS* become deprecated in favor of
+    # 'SSLContext.minimum_version' from Python 3.7 onwards, however
+    # this attribute is not available unless the ssl module is compiled
+    # with OpenSSL 1.1.0g or newer.
+    # https://docs.python.org/3.10/library/ssl.html#ssl.SSLContext.minimum_version
+    # https://docs.python.org/3.7/library/ssl.html#ssl.SSLContext.minimum_version
+
+    # these _set_mimimun_version and _set_maximum_version depend on the validation
+    # already performed in `Security._set_tls_version_field`,
+    # and that they only apply to freshly created ssl.SSLContext instances in
+    # _get_tls_context
+    def _set_minimum_version(ctx: ssl.SSLContext, version: ssl.TLSVersion) -> None:
+        ctx.minimum_version = version
+
+    def _set_maximum_version(ctx: ssl.SSLContext, version: ssl.TLSVersion) -> None:
+        ctx.maximum_version = version
+
+else:
+
+    def _set_minimum_version(ctx: ssl.SSLContext, version: ssl.TLSVersion) -> None:
+        # if the ctx.maximum_version attribute is unsupported then we can infer
+        # that TLS 1.3 is not supported.
+        # _set_tls_version_field enforces that version is TLSVersion.TLSv1_2,
+        # or TLSVersion.TLSv1_3
+        if version is not ssl.TLSVersion.TLSv1_2:
+            raise ValueError(f"Unsupported TLS/SSL version: {version!r}")
+        ctx.options |= (
+            ssl.OP_NO_SSLv2 | ssl.OP_NO_SSLv3 | ssl.OP_NO_TLSv1 | ssl.OP_NO_TLSv1_1
+        )
+
+    def _set_maximum_version(ctx: ssl.SSLContext, version: ssl.TLSVersion) -> None:
+        # if the ctx.maximum_version attribute is unsupported then we can infer
+        # that TLSv1_3 is not supported.
+        # _set_tls_version_field enforces that version is TLSVersion.TLSv1_2,
+        # TLSVersion.TLSv1_3, or None
+        # _get_tls_context enforces that version is not None
+        if version is not ssl.TLSVersion.TLSv1_2:
+            raise ValueError(f"Unsupported TLS/SSL version: {version!r}")
+
+
 class Security:
     """Security configuration for a Dask cluster.
 
@@ -71,6 +121,12 @@ class Security:
     )
 
     def __init__(self, require_encryption=None, **kwargs):
+        if _OPENSSL_VERSION_INFO < (1, 1, 1):
+            warnings.warn(
+                f"support for {ssl.OPENSSL_VERSION} is deprecated,"
+                " and will be removed in a future release",
+                DeprecationWarning,
+            )
         extra = set(kwargs).difference(self.__slots__)
         if extra:
             raise TypeError("Unknown parameters: %r" % sorted(extra))
@@ -251,10 +307,11 @@ def _get_tls_context(self, tls, purpose):
             else:
                 ctx = ssl.create_default_context(purpose=purpose, cafile=ca)
 
-            if self.tls_min_version is not None:
-                ctx.minimum_version = self.tls_min_version
+            # the _set_tls_version_field method enforces that
+            # self.tls_min_version is TLSv1_2, or TLSv1_3
+            _set_minimum_version(ctx, self.tls_min_version)
             if self.tls_max_version is not None:
-                ctx.maximum_version = self.tls_max_version
+                _set_maximum_version(ctx, self.tls_max_version)
 
             cert_in_memory = "\n" in cert
             key_in_memory = key is not None and "\n" in key
diff --git a/distributed/tests/test_security.py b/distributed/tests/test_security.py
index 49fa001f571..e4abfa46301 100644
--- a/distributed/tests/test_security.py
+++ b/distributed/tests/test_security.py
@@ -110,6 +110,14 @@ def test_min_max_version_config_errors(field):
             sec = Security()
 
 
+def test_invalid_min_version_from_config_errors():
+    with dask.config.set({"distributed.comm.tls.min-version": None}):
+        with pytest.raises(
+            ValueError, match=r"tls_min_version=.* is not supported, expected one of .*"
+        ):
+            Security(tls_min_version=ssl.TLSVersion.MINIMUM_SUPPORTED)
+
+
 def test_kwargs():
     c = {
         "distributed.comm.tls.ca-file": "ca.pem",