Buffon was enraged by English referee Michael Oliver’s decision to award Real Madrid a stoppage-time penalty kick during the second leg at the Bernabeu.
The Italian lost control, screaming at and jostling the Englishman until he was shown a red card.
Cristiano Ronaldo converted the spot-kick and Real lost the match 3-1 to win the tie 4-3 on aggregate.
“The UEFA Control, Ethics and Disciplinary Body has decided to suspend Juventus player Gianluigi Buffon for three UEFA competition matches for which he would be otherwise eligible,” UEFA said in a statement on its website on Tuesday.
The 40-year-old Buffon, who left Juventus after 17 seasons at the club, criticised Oliver after the match.
He said the referee had been out of his depth, should have been in the stands eating crisps and must have a garbage bin for a heart.
UEFA also banned AS Roma supporters for two away games after fan violence left one Liverpool supporter in a critical condition ahead of the Champions League semi-final at Anfield.
Roma’s ban for the second match has been deferred under a probationary period of two years, UEFA added in the statement.
The Italian club were also fined 50,000 euros (about $58,330).
Merseyside Police arrested two men from Rome in April after Liverpool supporter Sean Cox was left with serious injuries following an attack.