"I don't think it's anything long term," Rays manager Joe Maddon said after a 5-3 victory over the Padres. "He probably will not play [Friday]. I don't know about his availability."
Crawford grounded out in the first inning Thursday and left one inning later. He hurt the shoulder making a throw to the plate Wednesday.
"Right now my shoulder is a little sore," Crawford said after Thursday's game. "We just want to treat it and try to get it well. I tried to get it loose and get ready for the game, but it was one of those things it wasn't feeling better so I just came out."
The AL player of the week for the period that ended June 20 has nine hits in his last 20 at-bats. Crawford is among the leaders in the majors this season with 26 stolen bases.
"It's very frustrating because I don't like to miss games," Crawford said. "It shouldn't be anything major, I hope."
The Rays had been carrying three catchers.
"Having the three catchers has been a wonderful luxury," Maddon said. "Especially with what's going on with Carl right now, we had to bolster the outfield a bit."
Joyce, who hit .293 with three homers and 12 RBIs in 25 games with Durham, will start Friday against Arizona. He began the season on the disabled list with a strained right elbow.