The Ravens have allowed an average of 295 yards passing to McCown, who has thrown four touchdowns and no interceptions against them.
"He's been on fire against us," coach John Harbaugh said Monday a few hours after the Browns made the announcement.
McCown's first start against Baltimore came in 2013, when he led the Chicago Bears to a 23-20 win for then-coach Marc Trestman (who is now the Ravens offensive coordinator). McCown threw for 216 yards and one touchdown.
Two years later, McCown passed for 457 yards against the Ravens in a 33-30 victory for the Browns. He was 36-of-51 (70.5 completion rate) for two touchdowns and a 111.3 rating.
One of those touchdowns was McCown lofting a ball toward the end zone before getting hit. The pass was remarkably pulled in by tight end Gary Barnidge with his legs.
"I just remember this guy having no conscience and just throwing the ball in there," Harbaugh said. "We have a lot of respect for him."
That same season, he threw for 212 yards and one touchdown in a 33-27 loss to the Ravens.
In addition to the numbers, the change in quarterback styles will cause the Ravens to adjust. Baltimore had been preparing for a mobile quarterback like Griffin all offseason, and the Ravens probably didn't have to switch up much after playing Tyrod Taylor in the opener.
Now, Baltimore has to alter its game plan for a pocket passer who's done well against the Ravens in the past.
"We know what kind of a player he is," Harbaugh said. "We know how good he is. And he's been super-good against us. So, we know we're going to have our hands full. It will be all hands on deck to get ready for the offense led by Josh McCown."