However, he told reporters he will return to the lineup Saturday.
Prior to Friday's game, Wright played catch and hit indoors.
"I would have liked to have been in the lineup," he said. "I have knowledgeable people in my corner that are holding the reins on me a little bit to make sure I don't do something. You don't want to injure something more."
The Mets are 2-5 in the seven games Wright has been active, but not playing.
"The team hasn't played all that well, and obviously they're playing a man down," he said. "So I feel terrible about that, but I don't make those decisions."