The right-hander left his start Friday at Kansas City after three scoreless innings and 39 pitches due to elbow stiffness.
"There's a pretty good chance we'll skip his next start," manager Eric Wedge said on Saturday.
Reyes said his elbow felt better on Saturday, but the Indians will likely be cautious because of his prior elbow problems. He was on the St. Louis Cardinals disabled list earlier this season with an elbow injury.
The elbow was "a little stiff" warming up Friday, Reyes said.
"I tried to do everything I could to loosen up, but it just wasn't happening. We're just being cautious and trying not to push it too much. It felt pretty good my last few starts. This is kind of a new thing."
Reyes is 2-1 with a 1.83 ERA in six starts with the Indians since being acquired in a July 26 trade with the Cardinals.
If Reyes does not start Wednesday against the Orioles, the Indians will likely call up left-hander Scott Lewis, who is 6-2 with a 2.33 ERA in 13 starts at Double-A Akron, which is in the Eastern League playoffs.
Indians right-hander Jake Westbrook, who went on the disabled June 3 and is out for the season after having Tommy John surgery, had arthroscopic surgery on his right hip Friday in Nashville, Tenn. He will be on crutches for about four weeks.