Villa revealed a "significant" coronavirus outbreak on 7 January, the day before it was due to face Liverpool in the FA Cup.
While Villa still went ahead with that match, fielding a squad made up entirely of youth players, its Premier League meeting with Tottenham on Thursday (AEDT) was not able to go ahead.
The Premier League decided at the start of the week to switch that game with Spurs versus Fulham, another match that had previously been postponed due to a COVID-19 outbreak at Craven Cottage last month.
It was always a possibility Villa's hosting of Everton could fall victim as well, and with several of the club's players and staff still in isolation, the Premier League made the decision to postpone.
The league also announced a new date for Villa's clash with Newcastle United, which would have been played on 4 December were it not for a coronavirus outbreak at St James' Park.
Now the game is set to take place on January 23, while the Everton match will be rearranged at a later date.