The two sides will go head-to-head for a place in the quarter-finals, having been pitted together in this afternoon's draw in Lausanne.
Led by former France Head Coach Phillippe Saint-Andre, the French outfit currently lie 12th in the Top14, just one point above the relegation play-off position.
However, Les Cistes are still able to boast a star-studded squad, including World Cup-winning fly-half Handre Pollard, France number eight Louis Picamoles and former French captain Guilhem Guirado.
Glasgow have the edge in the historical meetings between the two teams, having emerged victorious on five of the eight occasions the pair have come up against each other in European competition.
Indeed, the two teams have previous in the Challenge Cup, with the first two meetings between the sides having come in the 2003/04 edition of the competition.
Tries from Sean Lamont, Donnie Macfadyen and Sam Pinder saw the Warriors earn a 30-11 win in France, before Lamont's brace and scores from Andy Henderson and Gordon Bulloch secured a 38-13 triumph at Hughenden.
The most recent clash with Montpellier came in the 2017/18 season, with the French side doing the double over the Warriors in the Heineken Champions Cup group stages.
It will be a first foray into the Challenge Cup since the 2006/07 season for the Warriors, having reached the quarter-finals on their previous entry into the competition.
Should they overcome Montpellier, Glasgow will be rewarded with a home quarter-final against the winner of the round-of-16 tie between Benetton and Agen on the weekend of 9/10/11 April.
It would be the first European knockout tie staged at Scotstoun, with each of the club's previous three European quarter-finals having been away ties.
Reacting to the draw, Glasgow Warriors Head Coach Danny 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."
Challenge Cup fixtures
Round of 16
Montpellier v Glasgow Warriors, GGL Stadium, 2/3/4 April - kick-off TBC
Quarter-finals
Montpellier or Glasgow Warriors v Benetton or Agen, GGL Stadium or Scotstoun, 9/10/11 April - kick-off TBC