Holders Exeter's Heineken Champions Cup match at Toulouse on Sunday has been cancelled because of a Covid-19 outbreak at the Chiefs.
Glasgow's home fixture against Lyon on Saturday has also been called off - because the Warriors played Exeter last weekend.
European bosses will now meet to decide the outcomes of the cancelled games.
It is envisaged that the matches cannot be rearranged because of fixture congestion.
A European Professional Club Rugby (EPCR) statement said: "EPCR has been informed that a number of Exeter Chiefs players and staff have tested positive for Covid-19.
"In accordance with public health guidelines, the club will not be able to send a matchday squad to fulfil its Heineken Champions Cup round 2 fixture against Toulouse at Stade Ernest Wallon on Sunday (20 December).
"The Pool B match is therefore cancelled."
Twenty Glasgow players are self-isolating after facing Exeter, and a Warriors statement said this, along with "an extensive injury list", meant it was "not safe" to play Saturday's game against Lyon.
The Glasgow statement added: "Glasgow Warriors will now turn its attention to mitigating any further risks to its squad to protect the upcoming 1872 Cup fixtures against Edinburgh in the Guinness Pro14."
When Fiji's recent Autumn Nations Cup fixtures were cancelled because of a coronavirus outbreak among the team, their opponents were awarded a 28-0 victory.
The Champions Cup is using a new, shortened format this year with each side only playing two others home and away in the group stages.
After that, the top four sides in each of two 12-team pools will advance to the quarter-finals, making bonus points and points difference even more important in the pool stage.
The EPCR statement continued: "As per its Covid-19 protocol, EPCR will convene match result resolution committees to determine the results of the cancelled matches and the decisions of the committees will be communicated as soon as practicable."