The 38-year-old Sabathia had a stent inserted after a blockage was found in an artery from his heart. He has had a chronic right knee problem that has required several operations.
Sabathia, who is retiring after this season, is expected to miss his first two or three regular-season starts.
The 2007 AL Cy Young Award winner with Cleveland, Sabathia is 246-153 with a 3.70 ERA and 2,986 strikeouts in 18 major league seasons. He was 9-7 with a 3.65 ERA in 29 starts last season.