The 53-year-old former midfielder has undergone surgery to have a stent fitted into a blocked artery.
"After a wonderful day with my children yesterday in Inverness, I returned to Aberdeen only to suffer a heart attack in the early hours of this morning," he said.
"Feeling good today but resting in the hospital with its wonderful staff supporting me. Thanks for the concern and texts from my friends."
Cooper was a member of the legendary 1983 European Cup Winners' Cup winning side.