Wright will be the designated hitter Monday night for Class A St. Lucie. He is scheduled to play in the field Tuesday.
New York general manager Sandy Alderson said after New York's 4-3 loss at Tampa Bay Sunday that Wright will play five innings in both games.
There has been no timetable announced for when Wright could rejoin the Mets.
''This is all new to all of us,'' New York manager Terry Collins said. ''We don't know how David is going to react. He's feeling great. He thinks it's going to be fast, but he doesn't know either. We'll have to take it day by day as we've said all along. There are no numbers set down for this guy, none. ''
Wright has played in just eight games this season.