diff --git a/airflow/utils/log/logging_mixin.py b/airflow/utils/log/logging_mixin.py
index 442fecd0363c8..f3b490e6a3bcf 100644
--- a/airflow/utils/log/logging_mixin.py
+++ b/airflow/utils/log/logging_mixin.py
@@ -68,6 +68,7 @@ def _set_context(self, context):
             set_context(self.log, context)
 
 
+# TODO: Formally inherit from io.IOBase
 class StreamLogWriter(object):
     encoding = False
 
@@ -83,6 +84,16 @@ def __init__(self, logger, level):
         self.level = level
         self._buffer = str()
 
+    @property
+    def closed(self):
+        """
+        Returns False to indicate that the stream is not closed (as it will be
+        open for the duration of Airflow's lifecycle).
+
+        For compatibility with the io.IOBase interface.
+        """
+        return False
+
     def write(self, message):
         """
         Do whatever it takes to actually log the specified logging record