Reyes was told the results of Thursday's team physical showed he may have an overactive thyroid.
The next round of tests will be conducted in New York and Reyes will be sidelined until the results are known, which could be as late as Wednesday, the team said.
"I don't know what's going on, this is the first time I've ever had something like this," Reyes said on the team's website (http://newyork.mets.mlb.com.) Friday.
"I have to be worried. I can't do anything."
The two-times All-Star came to the ballpark Friday expecting to make his spring debut against the Florida Marlins.
(Writing by Steve Ginsburg in Washington)