An MRI on Reyes' elbow by team physician Dr. Mark Schickendantz revealed an inflamed ulnar nerve.
"We feel it will be beneficial for him to have surgery," Indians head athletic trainer Lonnie Soloff said Monday. "But Anthony will seek a second opinion in Los Angeles later this week from Dr. Lewis Yocum."
Soloff said recovery time from a procedure to transpose the ulnar nerve typically is four to six months.
Soloff also said left-hander Aaron Laffey will be sidelined four to six weeks with a strained right oblique and that designated hitter Travis Hafner has been recalled from his rehab assignment in the minors because of back soreness.
Right-hander Joe Smith, out since May 2 with a strained right rotator cuff, threw a 40-pitch bullpen session and could go to the minors to rehab next week.
Reyes left his last start Friday night in Cincinnati after walking a career-high six and hitting another batter during three innings. He threw only 23 of 59 pitches for strikes.
Laffey was hurt in the same game. He grabbed his right side after making a pitch in the eighth inning and was removed from the game.
Hafner, sidelined since April 29 with right shoulder soreness, returned to Cleveland from Triple-A Columbus, where he started a rehab assignment last Monday. He is expected to take batting practice with the Indians the next two days and if all goes well, return to Columbus.
Hafner had shoulder surgery in October, but opened this season with the Indians. In 17 games, he hit .270 with four homers and eight RBIs.
Smith, acquired from the New York Mets in December, worked only 6 1/3 innings before being sidelined.
"He threw all his pitches today and will throw a simulated game Wednesday," Soloff said. "If that goes well, he could then start a rehab assignment."
Soloff also said that right-hander Jake Westbrook is progessing well at the Indians' spring training complex in Arizona. Westbrook had Tommy John surgery 11 months ago and is scheduled to throw three innings or 50 pitches on Wednesday.