Couch, who suffered a fractured right fibula late in the first quarter of Sunday's win over Atlanta, was fitted for a cast Monday morning.
"He is going to be out for a pretty significant amount of time," said Browns coach Butch Davis.
Most likely, Couch would miss between four and six weeks. That means he will not be available, no matter how deep the Browns go into the playoffs.
"That is a huge blow to this football team," said Davis. "Without Tim's leadership, we certainly would not be in the playoffs."
Davis said the Browns will sign a free agent to serve as the emergency quarterback and take the some of the practice load off of Booty when running the scout team.
"We have discussed three or four different guys," said Davis. "We will talk to them, give them physicals and find out where they are."
The most likely scenario would have the Browns re-signing Kevin Thompson, who spent the last two seasons with the Browns and was released at the end of training camp. The Browns could sign a third quarterback by the end of the day.