The teams had been due to meet for the first of the traditional festive PRO14 double-header between the clubs on December 27, with the return match in the Capital fixed for January 2.
But the clash in Glasgow’s West End will now not go ahead, with at least four of Danny Wilson’s players testing positive for Covid-19.
Warriors’ European Champions Cup meeting with Lyon, originally scheduled for Saturday December 19, has already been called off along with Exeter Chiefs' meeting with Toulouse and with no space in the calendar to reschedule the fixtures, competition organisers European Professional Club Rugby will convene a match resolution panel to decide the result of the games, with one possible outcome a 28-0 defeat for Glasgow.
A total of 20 Glasgow players were advised to self-isolate after an outbreak of the virus among the Chiefs, who defeated Warriors 42-0 at Sandy Park in last week's Champions Cup game, and another defeat would all but scupper the Scotstoun side’s chances of reaching the quarter-finals.
It is understood that Glasgow bosses are awaiting the results of a further round of testing.
A statement from PRO14 chiefs read: “Having considered all the evidence, the PRO14 Rugby Medical Advisory Group has deemed that this fixture cannot go ahead as scheduled.
"PRO14 Rugby will examine potential dates in early 2021 to reschedule the game.”
An Edinburgh spokesperson added: “We wish Glasgow Warriors the very best and those affected in these difficult circumstances a swift return to full health.”