Kansas City said Thursday the 25-year-old was operated on a day earlier by Dr. James Andrews, who repaired ligament damage in Collins' left elbow.
Collins made his spring training debut against Texas on March 4 and left after two outs.
"Timmy threw a curveball, and that's when he first started feeling it," manager Ned Yost said at the time. "Then he threw seven or pitches after and it kept getting tighter."
Collins had an MRI that revealed ligament damage.
He topped AL relievers with 93 strikeouts in 2012, but a left flexor strain last April put him on the disabled list for a month. He went 0-3 with a 3.86 ERA in 22 regular-season games and had a 3.18 ERA in four postseason games, including three World Series appearances.