The match was scheduled to take place at Scotstoun at 7pm but the United Rugby Championship announced that the game was off at around 1.15pm.
The clubs are due to meet in the second leg at the DAM Health Stadium on Sunday, January 2 but there must now be a question mark over that game too.
Edinburgh have also been hit by a number of Covid cases this week and head coach Mike Blair was due to miss tonight’s game because he was isolating as a close contact.
No new date has been announced for the first leg.
A statement from the URC said: “The game was due to take place on Monday, December 27 in Glasgow, however, a number of positive Covid-19 cases within the Glasgow Warriors squad have been reported by the club.
“The URC Medical Advisory Group has liaised with Glasgow Warriors and Public Health Scotland and deemed that the fixture cannot go ahead as scheduled.
“The United Rugby Championship will now consider available dates to reschedule the game.”