Instead of calling up a pitcher from the Minors, manager Bobby Valentine will call on lefty reliever Franklin Morales to fill in for Beckett.
"Josh has a little inflammation in his right shoulder," said Valentine. "The training room thinks that it's best that he's rested a little."
Beckett declined comment after Friday's game, saying he would elaborate on Saturday.
In 12 starts this season, Beckett is 4-7 with a 4.14 ERA. He didn't show any signs of injury in his last start, a loss to the Marlins in which he allowed four runs over the first two innings, then didn't allow a hit across his final five frames.
"He may get some tests," Valentine said. "I think they want to do a baseline [exam] to figure out where we are with that whole situation, so there might be tests."
Beckett missed a start earlier this season with a mild lat strain, but the team admitted to being overly conservative on that occasion, saying the righty could have started.
"He didn't feel it during a side [session]; just in the training room," Valentine said. "When they test him, they felt he's not quite recovering on a five-day rotation right now."
Morales last started a Major League game in 2009. As a reliever this season, he is 0-1 with a 3.04 ERA, holding opponents to a .236 average.
On June 3 at Toronto, Morales pitched a season-high 4 1/3 innings.