Joyce, who was scratched from the lineup due to flu-like symptoms before Sunday's game, said the left side of his back got tight. He added that he did not feel he had injured himself seriously.
"Hopefully I can come in tomorrow and get some work done on it and get ready to go," Joyce said. "I told [Rays manager] Joe [Maddon] I didn't think it was a pull or anything. I just wanted to be smart. It's just frustrating."
Sean Rodriguez was inserted into Joyce's cleanup spot in the order and came in to play third base in the bottom of the fifth. Third baseman Will Rhymes shifted to second base and second baseman Ben Zobrist moved to right field.
Bill Chastain is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.