The Royals announced that Altavilla (oblique) will begin a minor-league rehab assignment with Triple-A Omaha on Tuesday.
Altavilla hasn't pitched since June 20 after suffering a strained right oblique and will begin a rehab stint Tuesday. However, he won't be eligible to return from the injured list until Aug. 19, so his stay at Omaha will last multiple weeks. The right-hander allowed six runs in 3.2 big-league innings this season.