Villa were forced to close their Bodymoor Heath training ground last week after a "significant" outbreak which saw 10 first-team players forced to self-isolate.
Dean Smith's team had to field their youth team for their FA Cup tie with Liverpool, which they lost 4-1, and with the situation showing no signs of improvement, Wednesday's match with Spurs has been called off.
The Premier League confirmed Spurs will instead play Fulham at the Tottenham Hotspur Stadium at the same time on Wednesday. The match was originally postponed on December 30.
As a result of the re-arrangement, Fulham's match against Chelsea moves from Friday to 5.30pm on Saturday, live on Sky Sports, while Villa vs Everton moves from Saturday to midday on Sunday, also live on Sky Sports.
A Premier League statement read: "Following Aston Villa's request to rearrange the fixture, and due to the number of players and staff who have either tested positive for COVID-19 or have been placed in isolation by the club, the Premier League had no other option than to reschedule the game."
The Premier League added it had enhanced its Covid-19 protocols with immediate effect this week, in addition to reimplementing a twice-weekly testing programme.
A Spurs club statement said: "Everyone at Tottenham Hotspur sends their best wishes to Aston Villa for a safe and speedy recovery to all those who are affected."
Tottenham head coach Jose Mourinho had challenged the Premier League to "show leadership" and not punish Tottenham with further postponements over coronavirus concerns.
Mourinho said it would be "completely impossible" for another one of Spurs' league games to be cancelled and said teams should be ready to play with the minimum 14 players.
Details of a new date for Tottenham's match at Villa Park will be confirmed in due course.
Sky Sports News reporter Rob Dorsett on the Pitch to Post Preview Podcast:
"What has happened at Aston Villa is what every club in the land has been fearing. They've been really badly affected by coronavirus and what hit them this time last week.
"[Even pushing the Everton game back to Sunday] makes it really tight because, by my reckoning, all the players that have tested positive or that have been self-isolating because of the outbreak at the training ground will be clear of that 10 day isolation period on Friday January 15.
"I think that's why the Premier League have agreed to push it back a day - because it would have been a big ask to suddenly go and play the game the day after. As it is, Villa's players might only have two training sessions - and one of those only a light one the day before - having not been together for 10 days.
"It's how a lot of clubs are trying to cope and keep the games going, and Villa have managed it for the Everton game, albeit not in an ideal scenario.
"They will be tested again 48-72 hours before the game. We know 10 first team players have actually tested positive for it but we don't know how poorly they are. Even if they are clear of the disease by then, will they be fit to play football? Will they have done any training at all in that 10-day period?
"It is a real blow to them, too, because they were absolutely flying. You look at that Man Utd game, which they narrowly lost, they drew at Chelsea before that, then before that there were two 3-0 victories against Crystal Palace and West Brom.
"They were scoring goals, looking really solid at the back - that's what's changed between now and the relegation battle of last season, just how tight they are at the back. That's providing the platform for the likes of Jack Grealish, John McGinn, and Ross Barkley when he's fit, to go and sparkle and create goals and Ollie Watkins, who has started his Villa career very well.
"You just hope this doesn't derail them. Every Villa fan will hope that this coronavirus outbreak is a blip. But at the moment it's an unknown quantity."
Tue Jan 12: Sheff Utd vs Newcastle - Kick-Off 6pm
Tue Jan 12: Wolves vs Everton - Kick-Off 8.15pm
Thur Jan 14: Arsenal vs Crystal Palace - Kick-Off 8pm
Sat Jan 16: Leeds vs Brighton - Kick-Off 3pm
Sat Jan 16: Fulham vs Chelsea - Kick-Off 5.30pm
Sun Jan 17: Aston Villa vs Everton - Kick-Off 12.00pm
Sun Jan 17: Sheff Utd vs Tottenham - Kick-Off 2pm
Sun Jan 17: Liverpool vs Man Utd - Kick-Off 4.30pm
Sun Jan 17: Man City vs Crystal Palace - Kick-Off 7.15pm
Mon Jan 18: Arsenal vs Newcastle - Kick-Off 8pm
Tue Jan 19: Leicester vs Chelsea - Kick-Off 8.15pm
Wed Jan 20: Leeds vs Southampton - Kick-Off 6pm
Thur Jan 21: Liverpool vs Burnley - Kick-Off 8pm
Sat Jan 30: Arsenal vs Man Utd - Kick-Off 5.30pm
Sat Jan 30: Southampton vs Aston Villa - Kick-Off 8pm
Sun Jan 31: Leicester vs Leeds - Kick-Off 2pm
Sun Jan 31: West Ham vs Liverpool - Kick-Off 4.30pm
It couldn't be simpler: we will have free-to-watch match highlights of every Premier League game on the Sky Sports website, app, and the Sky Sports YouTube channel shortly after full-time of every fixture.
In addition, Sky subscribers will also be able to enjoy in-game clips from Sky Sports matches in our Digital match blogs.
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