Clifford, 52, checked himself into a Charlotte hospital after reporting chest pains during dinner Thursday. Doctors determined Clifford need two stents placed in his heart and carried out the operation Friday.
The Bobcats said Clifford was "resting comfortably" and would be able to rejoin the team "soon."
However, he will miss Friday's game, leaving Charlotte associate head coach Patrick Ewing to coach the Bobcats against the Knicks,. Ewing played for New York for 15 seasons.
Clifford is the third major sports coach to be hospitalized in the last week.
Denver Broncos Coach John Fox underwent heart surgery in Charlotte, and was discharged from a hospital Friday, and Houston Texans Coach Gary Kubiak collapsed at halftime of his team's game last Sunday and has been diagnosed as having had a minor stroke.
Both NFL coaches have been replaced on an interim basis by their defensive coordinators.