Church was injured trying to break up a double play May 20 against the Braves. He has not started a game since then but went 1-for-4 as a pinch hitter, accompanying the team on its trip to Colorado and then back to New York.
He reported not feeling well after both plane trips and the Mets said he would not play again until 48 hours after he is symptom-free.
Church missed a week in spring training when he was diagnosed with a concussion after colliding with teammate Marlon Anderson on a pop fly in an exhibition game.
Mets general manager Omar Minaya defended the team's handling of Church's injury and said he doesn't regret immediately placing the outfielder on the disabled list.
"I don't second-guess myself," Minaya told reporters, according to the New York Times. "Those things happen. We have to make those decisions on a daily basis throughout the season. A lot of guys are day to day and you ask yourself, Do you do it?"
"These things happen as far as making decisions on questions whether a guy's going to be OK or not OK on a day-to-day basis. It's part of the season."
Information from The Associated Press was used in this report.