The draw, took place in Monaco, placed United and Roma alongside Sporting Lisbon and Dynamo Kiev.
A united fan was stabbed in the first-leg in Rome and clashes between supporters from both sides took place just outside Old Trafford in the return match.
United romped to a 7-1 victory in Manchester, leaving the Italian capital side suffering the biggest European defeat in their country's history.
Title holders AC Milan are set to face former Champions Benfica in group D while silver-medalists Liverpool were placed in Group A with Portugal's second representatives Porto.
Only one slot remains to be occupied by either Sevilla or AEK Athens. Their game was postponed in mourning to the death of Sevilla's defender Antonio Puerta earlier this week.
The full draw
Group A
Liverpool (ENG)
Porto (POR)
Marseille (FRA)
Besiktas (TUR)
Group B
Chelsea (ENG)
Valencia (ESP)
Schalke 04 (GER)
Rosenborg (NOR)
Group C
Real Madrid (ESP)
Werder Bremen (GER)
Lazio (ITA)
Olympiakos (GRE)
Group D
AC Milan (ITA)
Benfica (POR)
Celtic (SCO)
Shakhtar Donetsk (UKR)
Group E
Barcelona (ESP)
Lyon (FRA)
Stuttgart (GER)
Rangers (SCO)
Group F
Man Utd (ENG)
Roma (ITA)
Sporting Lisbon (POR)
Dynamo Kiev (UKR)
Group G
Inter Milan (ITA)
PSV Eindhoven (NED)
CSKA Moscow (RUS)
Fenerbache (TUR)
Group H
Arsenal (ENG)
Sevilla (ESP) or AEK Athens (GRE)
Steaua Bucharest (ROM)
Slavia Prague (CZE)