Publicist Michael Jensen tells City News Service that the 72-year-old had a cardiac catheterization last week to fix a blocked coronary artery.
He's expected to make a full recovery, but concerts planned for February 20 and 21 at Great American Music Hall in San Francisco, as well as shows scheduled in West Hollywood, will be moved to April.
Crosby says he'll be ready to perform with the group Crosby, Stills and Nash on a tour that kicks off in Richmond, Va., on March 4.
Crosby underwent a liver transplant in 1994.
In a statement, the performer says he is "once again a very lucky man."