Atletico Madrid and Bayern Munich were drawn together in the other standout tie, while holders Chelsea will face French champions Lille.
PSG will be at home in the first leg in February in a tie that will see Lionel Messi and Cristiano Ronaldo come up against each other.
Atletico Madrid and Bayern Munich were drawn together in the other standout tie, while holders Chelsea will face French champions Lille.
Messi moved to Paris in August just before his old rival Ronaldo returned to Old Trafford for a second spell
United famously beat PSG in the last 16 in 2018/19 at the start of Ole Gunnar Solskjaer's reign as manager, recovering from a 2-0 loss at home in the first leg to win the return 3-1 and advance on away goals.
The clubs also met in the group stage last season, with the away side winning on each occasion.
Despite the signing of Messi, Mauricio Pochettino's PSG finished second in their group this season behind Manchester City, while United topped Group F ahead of Villarreal.
Pep Guardiola's City will play Villarreal, who beat United on penalties in last season's Europa League final and qualified for the last 16 ahead of Atalanta.
Meanwhile Liverpool will play Austrian champions Red Bull Salzburg, who are through to the knockout phase for the first time.
Record 13-time European champions Real Madrid were drawn against two-time former European Cup winners Benfica, with the first leg in Lisbon.
Inter Milan play Ajax and Portuguese champions Sporting will take on Juventus.