diff --git a/pandas/io/parsers.py b/pandas/io/parsers.py
index a3ff837bc7f52..233fafa918722 100755
--- a/pandas/io/parsers.py
+++ b/pandas/io/parsers.py
@@ -1930,6 +1930,8 @@ def __init__(self, src, **kwds):
                 ]
             else:
                 self.names = list(range(self._reader.table_width))
+        elif self.prefix:
+            raise ValueError("argument prefix must be None if no headers provided")
 
         # gh-9755
         #