Weeden could be ready to practice and play as early as next week, a source told ESPN NFL Insider Adam Schefter on Thursday.
Coach Rob Chudzinski said after Friday's practice that it's "highly unlikely" that the second-year QB will need surgery. Weeden was injured in Sunday's loss at Baltimore. On Thursday, he visited a hand specialist, who confirmed the diagnosis of a sprain and did not find any further damage.
Chudzkinski said the team will re-evaluate Weeden next week and "play it by ear" as to when he plays again.
On Wednesday, Chudzinski named third-stringer Brian Hoyer the starter for Sunday in Minnesota, and said Weeden's job was not guaranteed when he returned.
Weeden seemed surprised to learn his job wasn't safe, and Chudzinski said he has spoken to the 29-year-old about the situation.
Weeden injured his thumb when he banged it on the helmet of teammate John Greco during the fourth quarter of Sunday's 14-6 loss to Baltimore.
"You never want to get hurt," said Weeden, who was sacked 11 times in Cleveland's two losses. "I don't care when it is, could be the 16th game or the first game, as a player, you want to be out there. So yeah, it is frustrating. Even though the results weren't there offensively, we were starting to do some better things."
Weeden finished 21-of-33 for 227 yards against the Ravens, but Cleveland's offense sputtered for the second week in a row. The Browns missed chances to make big plays, none bigger than when Weeden missed running back Chris Ogbonnaya wide open down the left sideline.
ESPN NFL Insider Adam Schefter and The Associated Press contributed to this report.