Wright broke the pinkie finger of his right hand diving back to a base in Monday's game against the Nationals.
He was examined by a hand specialist for the second straight day Thursday. The Mets said in a statement the team's No. 3 hitter was cleared to resume baseball activities "as tolerated."
The Mets won't make a determination on Wright's status for the first game of the series against the Phillies until before the game on Friday.
The Mets got out of the gates to a 4-0 start before Wright missed the past two games due to the injury. New York dropped both games. Wright is hitting .583 with one homer run and 4 RBI in four games.