Nathan, who is in the final season of a two-year $20 million contract with the Tigers, confirmed the surgery Thursday. He logged 35 saves in 2014 for the Tigers.
Nathan, 40, logged one save this year in the season opener at Minnesota, but went on the disabled list the next day with elbow pain. He exited after 10 pitches with a sharp pain in his right arm on a minor league rehab assignment on April 22 with Toledo.
He was diagnosed with an ulnar collateral ligament tear and a flexor pronator tear. Dr. Keith Meister, the Texas Rangers team physician, performed the surgery.
With Nathan out, Joakim Soria has an American League-leading nine saves in as many opportunities. The nine saves is a Tigers' record for April.