Rays manager Kevin Cash said Franco wanted to play, but they decided that "if we can buy him an extra day, I don't think it'll hurt."
Franco trotted into third slowly in the opening game of a day-night doubleheader on Saturday. He was visited by a team trainer and Cash but stayed in the game. He finished with three hits in the 8-5 loss in the opener before sitting out the nightcap.
The Rays' 22-year-old star is hitting .305 with seven homers and 29 RBIs.
The Associated Press contributed to this report.