The game against Wolves was rejected by the league.
The application was turned down on Sunday morning before the 2pm kick-off.
The Blues had five players test positive for coronaviruses ahead of their home game against the Toffees on Thursday.
It is believed that there has been at least one positive case overnight.
A spokesman for the club said that they were deeply disappointed that their application was rejected, as they felt they had a strong case for the postponement of the game.
Six of this weekend's premier league games have been postponed due to the Covid-19 outbreak.
The league said that applications are assessed on a case-by-case basis and decisions are based on existing rules.
The only game to take place on Saturday was the 4-1 victory at injury-hit Leeds by the Gunners, which was followed by the abandonment of the home game against Burnley due to increased positive cases within the hosts' squad.
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The Covid crisis has led to games being called off, and Alan Pace wants more notice so that clubs and fans can plan accordingly.
There have been 10 postponements of games in the premier league so far.
The other matches on Sunday, which are live on Sky Sports, will go ahead as planned.
The round of fixtures was called off on Thursday by Thomas Frank in order to allow clubs to deal with the outbreak.
Talks between clubs and team managers will take place on Monday, with the Premier League resisting calls for a halt to the competition.
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There is a chance to watch the highlights from Thursday's game between the two teams.
After a run of just two wins from their last five games in the competition, the Blues trail league leaders Manchester City by four points.
The Carabao Cup quarter-finals will be played on Wednesday, before the Blues face Villa on Boxing Day.
What are the rules for postponements?
The Premier League board will only allow the rearrangement or postponement of a league match in exceptional circumstances according to the handbook.
The board make calls on a case-by-case basis, and by way of guidance from the league, permission for a postponement will not be granted if a club has more than 14 players available.
The ability of a club to field a team, the status of the Covid-19 outbreak at the club, and the ability of the players to safely prepare for and play the match are some of the factors that will be assessed by the league.
The board must consider the risks to the opposition and other people who the club may come into contact with.
