City, the last British side remaining in this season's competition, eased past Russian side Zvezda 2005 6-0 on aggregate in the previous round.
Three-time semi-finalists Brondby, who were seeded for Monday's draw, beat Austrian club St Polten in the last 32.
The first leg in Manchester will be held on 9 or 10 November, before the second leg on 16-17 November.
Manchester City have already clinched their first English league title this season and completed a domestic double with victory in the Continental Cup (League Cup).
Fellow English side Chelsea went out to German club Wolfsburg in the last 32, while Scottish sides Glasgow City and Hibernian were also knocked out at the same stage, after Welsh champions Cardiff Met went out in the qualifying rounds.
The 2016-17 final will be held in Cardiff on Thursday, 1 June.
Paris Saint-Germain (FRA) v BIIK-Kazygurt (KAZ)
Barcelona (ESP) v FC Twente (NED)
Slavia Praha (CZE) v Rosengard (SWE)
Manchester City (ENG) v Brondby (DEN)
Brescia (ITA) v Fortuna Hjorring (DEN)
Lyon (FRA) v FC Zurich (SUI)
Eskilstuna United (SWE) v Wolfsburg (GER)
Bayern München (GER) v Rossiyanka (RUS)
Manchester City have been drawn to face Danish side Brondby in the last 16 of the Women's Champions League.