PSG, who are into the last 16 for the sxith consecutive season, are runaway leaders of the French championship while United are struggling in sixth in the English Premier League following a 3-1 defeat at Liverpool on Sunday.
Lyon have not featured in the last 16 since 2012 and will confront one of the undisputed giants of European football: Barcelona has reached at least the quarter-final every year since 2007.
Defending champions Real Madrid will continue their quest for a fourth straight title against Ajax while last year's beaten finalists Liverpool will take on Bayern Munich.
There will be two other Anglo-German clashes. Tottenham Hotspur will play Borussia Dortmund and Shalke face Manchester City.
The two Italian sides Juventus and Roma will test their mettle against Atletico Madrid and Porto respectively.
"The road to Madrid has already been exciting," said draw host Pedro Pinto. "And those levels of excitement will remain high when the knockout phases begin in February."