Upton, who suffered a left shoulder strain Thursday in Baltimore, told manager Joe Maddon he just needed a little more time.
"He took some practice swings and felt pretty good," Maddon said. "Our main concern right now is a swing and a miss [which can aggravate the injury]. So we're just going to reserve him for pinch-hitting duty tonight."
Should the Rays get rained out Sunday, which is what the weather forecast suggests, Upton would be able to have four days of rest after the injury since the Rays have an off-day Monday. If the Rays aren't rained out Sunday, Maddon said it "kind of sounds like [Upton] will be" in the lineup.
Upton, replaced by Nathan Haynes in center field Saturday, is hitting .294 with three home runs and 21 RBIs this season.
Bill Chastain is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.