Zimmer, who is considered the Royals' fourth-best prospect by Baseball America, hopes to be pitching in games by May.
Zimmer has been rehabbing at the team's spring complex in Arizona all offseason.
Zimmer underwent arthroscopic surgery Tuesday after feeling tightness in his shoulder during Arizona Fall League play.
The MRI on
Zimmer felt tightness in his shoulder during a start in the Arizona Fall League this month and was shut down for the rest of the offseason.
Zimmer, who has 187 strikeouts in 152 2/3 minor league innings since 2012, has struggled to maintain health with his shoulder. He was limited to just 4 2/3 innings pitched in 2014.
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