Royals manager Ned Yost said he believes the injury was a "complete tear," according to MLB.com.
Collins has spent the last four seasons with Kansas City. He returned to the team this offseason on a one-year contract reportedly worth $1.475 million.
Collins suffered an elbow strain last April and pitched only 21.0 innings during the 2014 season.
During his first three seasons (2011-13), Collins recorded a 3.51 ERA while appearing in at least 65 games each season.
"It’s obviously very disappointing," general manager Dayton Moore said, according to The Kansas City Star. "Timmy’s been a very important part of our bullpen. We expected him to have a terrific year. So it’s a disappointment. We’re just going to have to cover it."
Kansas City opens the season on April 6 against the Chicago White Sox.