IRFU President John Lyons and Maurice Crowley, General Manager of AIB, were on hand to draw the teams out after the game.
Newly-crowned Ulster Senior League champions Ballynahinch, who knocked out cup holders Shannon, have earned a trip to Galwegians.
AIB League Division One champions Cork Constitution face a short trip to local rivals Dolphin in what promises to be one of the ties of the round.
All ties to be played on the weekend of February 14 and 15.
AIB Cup Quarter-Finals Draw:
Garryowen v Buccaneers
Galwegians v Ballynahinch
Young Munster v UCC
Dolphin v Cork Constitution