diff --git a/rq/scheduler.py b/rq/scheduler.py
index 17e2c5d..b55f728 100644
--- a/rq/scheduler.py
+++ b/rq/scheduler.py
@@ -13,8 +13,7 @@ from .registry import ScheduledJobRegistry
 from .utils import current_timestamp, enum
 from .logutils import setup_loghandlers
 
-from redis import Redis
-
+from redis import Redis, SSLConnection
 
 SCHEDULER_KEY_TEMPLATE = 'rq:scheduler:%s'
 SCHEDULER_LOCKING_KEY_TEMPLATE = 'rq:scheduler-lock:%s'
@@ -47,6 +46,10 @@ class RQScheduler(object):
         self._scheduled_job_registries = []
         self.lock_acquisition_time = None
         self._connection_kwargs = connection.connection_pool.connection_kwargs
+        self._connection_class = connection.__class__  # client
+        connection_class = connection.connection_pool.connection_class
+        if issubclass(connection_class, SSLConnection):
+            self._connection_kwargs['ssl'] = True
         self._connection = None
         self.interval = interval
         self._stop_requested = False
@@ -57,8 +60,8 @@ class RQScheduler(object):
     def connection(self):
         if self._connection:
             return self._connection
-        self._connection = Redis(**self._connection_kwargs)
-        return Redis(**self._connection_kwargs)
+        self._connection = self._connection_class(**self._connection_kwargs)
+        return self._connection
 
     @property
     def acquired_locks(self):