“After the latest round of Covid-19 testing, the club returned a number of positive cases, in addition to the four already reported on Christmas Day,” said City in a statement on their website.
“With the security of the bubble compromised, there posed a risk that the virus could spread further amongst the squad, the staff and potentially beyond.
“Based on strong medical advice the Premier League, in consultation with both clubs, have decided to postpone the fixture.”
Monday’s game had been slated to kickoff at 8 p.m. local time at Goodison Park in Liverpool.
An alternative date and kickoff time has yet to be decided, according to Everton.
The Premier League says further testing will be conducted on Tuesday.
Meanwhile Crystal Palace and Leicester City shared a 1-1 draw on Monday as the Premier League’s intense festive schedule of matches continued.
Wilfried Zaha’s superb finish then gave Palace the lead, before Harvey Barnes’ low shot late on secured Leicester a point, moving Brendan Rodgers’ side on to 29 points, three behind the Premier League defending champion.