Following the Rays' 8-2 win over Cleveland on Wednesday night, Upton informed manager Joe Maddon that he will sit out Thursday's day game against Cleveland and Friday's home game against Baltimore.
Upton was suspended by Major League Baseball a week ago for a tirade during a game May 4. He was originally scheduled to start serving his suspension last week, but decided to appeal.
He was fined $1,500 and suspended two games for slamming his bat and helmet to the ground. He had to be restrained after striking out for the fourth time.
Upton had two hits and two RBIs in Wednesday's win.