Manchester United have been drawn against Sevilla, Manchester City play Basel and Liverpool are up against Porto, but fellow group winners Tottenham Hotspur have a tough test in Italian champions Juventus.
Bayern Munich, who finished second to PSG in Group B, play Besiktas and Shakhtar Donetsk take on Roma.
The biggest tie of the round, though, sees Madrid -- winners in both 2016 and 2017 -- facing a PSG side widely considered among the leading contenders to win the trophy this season after bringing in Neymar, Kylian Mbappe and Dani Alves in the summer.
Madrid pay the price for a slow start to the season that saw them unexpectedly finish runners-up to Tottenham in the group stage.
English champions Chelsea have also suffered for having to settle for second place in their group behind Roma, with a match-up with Ernesto Valverde's revitalised Barcelona representing a significant hurdle if they are to progress.
Among the other Premier League clubs, United, City and Liverpool will all be favourites to reach the quarterfinal stage after avoiding Madrid and Bayern, but Spurs must overcome a Juve side who -- despite a relatively disappointing campaign so far -- have reached two of the last three finals.
Ties to be played Feb. 13, 14, 20 and 21 and March 5, 6, 12, 13
Juventus vs. Tottenham Hotspur
Basel vs. Manchester City
Porto vs. Liverpool
Sevilla vs. Manchester United
Real Madrid vs. Paris Saint-Germain
Shakhtar Donetsk vs. Roma
Chelsea vs. Barcelona
Bayern Munich vs. Besiktas