The Irish side, who fought to a 16-13 win over Toulouse in the 2008 final, face the tough task of fighting off two French teams in a group including the extra seventh qualification spot earned by the Top 14.
Clermont finished the French league regular season in first, while Montauban's seventh-placed finish took them to Europe's premier rugby competition for the first time in their history.
The trio will also face Sale Sharks, who came fifth in the Premiership.
Three-time champions and last season's runners-up Toulouse were drawn with British trio Bath, Glasgow and Newport.
Premiership play-off winners and former champions Wasps, meanwhile, drew Castres and Celtic League champions Leinster, along with Edinburgh.
The winners of each of the six pools will qualify for the quarter-finals along with the two best runners-up.
Munster [IRL], Sale [ENG], Clermont Auvergne [FRA], Montauban [FRA]
Wasps [ENG], Leinster [IRL], Castres [FRA], Edinburgh [SCO]
Leicester [ENG], Perpignan [FRA], Ospreys [WAL], Treviso [ITA]
Stade Francais [FRA], Llanelli [WAL], Ulster [IRL], Harlequins [ENG]
Toulouse [FRA], Bath [ENG], Newport Gwent Dragons [WAL], Glasgow [SCO]
Biarritz [FRA], Gloucester [ENG], Cardiff [WAL], Calvisano [ITA]