Catcher Ramon Hernandez was also out of the starting lineup because of a sprained left wrist.
Mora was hit by a bad-hop grounder during fielding practice. The third baseman had a similar injury during spring training, and had completely recovered before being struck in the same place Tuesday.
"I go like this, it hurts," he said, raising right arm.
Mora was replaced at third base by Aubrey Huff, who botched a grounder in the first inning. Huff went 1-for-4 with two strikeouts as the Orioles won 5-4.
Hernandez received a cortisone shot to relieve the inflammation in his wrist, which had been bothering him for two weeks. He said the injury causes him pain when he swings a bat.
Hernandez didn't anticipate being placed on the 15-day disabled list.
"We'll give it a couple of days to get the inflammation down and then we'll see where we're at," he said.
Manager Dave Trembley didn't rule out the possibility of inserting the catcher as a late-inning defensive replacement, and held out hope that the injury would not keep Hernandez out of the lineup for more than a day.
Information from The Associated Press contributed to this report.