As group winners, both United and PSG will be away in the first-leg matches, which are due to be played in February and they will host the second-leg games in March.
The draw, which took place at UEFA headquarters on Monday, also paired Liverpool with Porto and Manchester City with Basel.
Tottenham must travel to Italy after being drawn against Juventus, while Roma face Shakhtar Donetsk.
Chelsea, meanwhile, face a daunting task after they were handed a tie against Barcelona. Bayern Munich, meanwhile, will take on Turkish giants Besiktas.
Champions League last 16 games are provisionally scheduled to take place in February and March 2018.
The first legs will be contested on February 13/14/20/21 and the second legs will be played on March 6/7/13/14.