The match will go ahead on Sunday 13 December (ko 3.15pm) and it will be the second consecutive season that the two sides will face each other in the pool stages, with Glasgow the only side to prevent Exeter from taking victory in their title-winning campaign in 2019/20.
The Warriors then welcome Lyon to Scotstoun for their home opener a week later, as they host the French side on Saturday 19 December (ko 1.00pm).
The return fixtures see Glasgow travel to the Matmut Stadium on Saturday 16 January (ko 2.00pm), looking to repeat their victorious trip to Lyon two years ago.
The pool stage concludes with the visit of Exeter to Scotstoun on Sunday 24 January (ko 5.30pm), the two sides having shared a thrilling 31-31 draw back in January.
Due to current guidelines, EPCR expects all matches in the pool stages to be played behind closed doors.