The injury apparently is not serious, and the 29-year-old is out for precautionary reasons, sources told Matt Ehalt of Yahoo Sports.
Wheeler is one of the best starting pitchers who could be available for trade ahead of the July 31 trade deadline.
One team that has been asking the Mets about Wheeler is the Tampa Bay Rays, Puma reports.
The IL move is retroactive to Friday, so the earliest that the 2009 sixth overall pick could return is July 23, which could allow him to potentially make two starts before the deadline.
The Mets, who enter Monday's action 14 1/2 games behind the Atlanta Braves for first in the National League East, have reportedly spoken to the New York Yankees, Boston Red Sox, and Milwaukee Brewers about a possible trade involving the starter.
Wheeler, an impending free agent, has accrued 130 strikeouts in 119 innings with a 3.66 FIP for New York this season.