Hochevar, a converted starting pitcher, emerged as one of the best set-up relievers last season, posting a 1.92 earned run average over 70-1/3 innings, allowing 41 hits and striking out 82 batters.
The 30-year-old Hochevar will rest for two to three weeks before beginning a recovery program.
Royals manager Ned Yost was quoted in the report as saying that a return for the right-hander by the end of May was the "best-case scenario."
The Royals open the MLB season on March 31.
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