Upton was hit on the left triceps with two outs in the first inning by a pitch from Cleveland starter Paul Byrd. The initial assessment of the injury was a triceps contusion. X-rays on Upton's arm were negative.
Rays manager Joe Maddon said Upton got hit "right above the elbow."
"He couldn't really feel the grip, so we got him out of there and got some ice on it," Maddon said. "[It's] just sort of in a bad spot, where it was going to swell up very quickly, which it did. ... We'll see later, but we think he'll be fine."
Meanwhile, Iwamura left the game after experiencing lower back stiffness during an at-bat in the third inning.
"He got a little stiff, so I said, 'Get him out of there,'" said Maddon, who noted that Iwamura felt tight warming up prior to the game but did not say anything. "I plan on using him [Friday] night -- just pregame he felt a little tight."
After getting hit, Upton was met by assistant trainer Paul Harker, who appeared to be testing Upton's strength in his left arm by having him go through a series of squeezing exercises.
Moments later, Upton left the game and was accompanied to the visiting clubhouse by Harker.
Neither player was available for comment, as both already had returned to St. Petersburg, Fla., by the time the clubhouse was open.
Upton started the game as Tampa Bay's designated hitter. Ironically, the Rays scratched him from playing center field due to wet conditions and their desire for him to avoid any possible dangers resulting from those conditions.
Upton, who is the Rays' starting center fielder, entered Thursday's game hitting .357 with one home run and nine RBIs in 13 Grapefruit League games this spring.
Bill Chastain is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.