Newcastle says there are "several" players and staff members self-isolating after returning positive tests in recent days.
The club's training ground has been closed in an effort to contain the outbreak, which has hampered the squad's ability to train and prepare for Saturday's (AEDT) game at Villa Park.
Newcastle lodged a request with the Premier League to have the game moved, which was accepted.
In a statement, the Premier League Board said it agreed that Newcastle were "unable to train and adequately and safely prepare for their match on Friday".
The statement said: "The decision has been taken in consultation with Newcastle United and Aston Villa, and following extensive consultation with PHE [Public Health England] and Premier League medical advisors, with the health of players and staff the priority.
"All players and training ground staff will be re-tested this week and another meeting between the club, PHE and the Premier League will take place to assess the test results.
"The Premier League wishes those with COVID-19 a safe and speedy recovery and will rearrange the postponed fixture against Aston Villa in due course."
Newcastle said: "The match, which was set to kick off at 8pm (GMT) on Friday evening, will now be rescheduled and a new date and time will be confirmed in due course. Newcastle United would like to thank Aston Villa Football Club for its understanding.
❌ #NUFC's fixture at Aston Villa on Friday has been postponed following a significant increase in Covid-19 cases at the Magpies’ Training Centre.— Newcastle United FC (@NUFC) December 1, 2020
A new date and time for the game will be confirmed in due course.
"Newcastle United was one of the first clubs in the country to close its training ground prior to the first national lockdown in March and the club introduced comprehensive COVID-19 protocols in line with Premier League and government guidance to protect its players and staff ahead of Project Restart.
"While the club has continued to ensure strict adherence to these protocols, and despite previously experiencing only a very small number of isolated COVID-19 cases, positive test results have risen sharply in recent days."
Newcastle is 13th in the table, a point behind Aston Villa, which has played a game less.