Alcala (elbow) will begin a rehab assignment at Single-A Fort Myers on Tuesday.
Alcala has been on the injured list since April 12 with right elbow inflammation, so he'll likely require at least a handful of appearances in the minors before the Twins are comfortable activating him. The 26-year-old reliever is first eligible to return from the 60-day IL on June 10, according to Do-Hyoung Park of MLB.com.