The Scottish club have been drawn away in the one-legged tie which will be played on the weekend of April 2-3-4.
It’s a tough draw for Danny Wilson’s side against the French team who won the competition in 2016. Glasgow can take some comfort from the fact that Montpellier have not had the best of seasons domestically and are currently 11th in the Top 14
The club is bankrolled by French-Syrian billionaire businessman Mohed Altrad and their head coach is France great Philippe Saint-André.
Saint-André, formerly coach of the French national side, was originally brought in as Montpellier’s director of rugby, but took over as head coach when Xavier Garbajosa was sacked in January. Garbajosa had succeeded former Scotland coach Vern Cotter in the job.
Reacting to the draw, Glasgow coach Wilson said: “We’re looking forward to restarting our European campaign and taking on Montpellier at GGL Stadium.
“Montpellier have a strong star studded squad an it will be a really exciting challenge away from home.
“Having only played one game in the Champions Cup this season we look forward to the opportunity of playing another European fixture and all that it brings.”
Glasgow dropped into the second-tier Challenge Cup from the Heineken Champions Cup.
They lost their opening match in the elite competition 42-0 to holders Exeter Chiefs and were then handed a 28-0 ‘defeat’ in their cancelled match with Lyon.
The game was called off because 20 Glasgow players were isolating after a Covid-19 outbreak at Exeter.
If the Warriors can overcome Montpellier they will face a home tie against either Benetton or Agen in the quarter-finals on the weekend of April 9-10-11.
European Challenge Cup last 16
Dragons v Northampton
Ospreys v Newcastle
London Irish v Cardiff Blues
Harlequins v Ulster
Benetton v Agen
Zebre v Bath
Leicester v Connacht
Montpellier v Glasgow Warriors
European Challenge Cup quarter-finals
Montpellier or Glasgow Warriors v Benetton or Agen
Dragons or Northampton v Harlequins or Ulster
Zebre or Bath v London Irish or Cardiff Blues
Leicester or Connacht v Ospreys or Newcastle