A number of United players and staff returned positive results after a round of lateral flow testing on Sunday, with those results later confirmed by PCR testing.
United closed down first team operations at their Carrington training ground on Monday and delayed travelling to London for the fixture, which was due to be played at the Brentford Community Stadium on Tuesday evening.
A United statement said: “Following PCR confirmation of positive LFT Covid-19 tests among the first team staff and players, the outbreak requires ongoing surveillance.
“A decision was taken to close first team operations at the Carrington Training Complex for 24 hours to help minimise risk of further infection, and individuals who tested positive are isolating in line with Premier League protocols.
“Given cancellation of training and disruption to the squad, and with the health of players and staff the priority, the club requested the match to be rearranged. The Premier League board took the decision to postpone based on guidance from medical advisors.”
United’s first team squad, including players and staff, were tested upon returning from the 1-0 win at Norwich City, with the individuals concerned sent home from Carrington on Sunday.
It is understood that all those to have tested positive returned negative tests before making the trip to Carrow Road.
Club sources claim it is too early to say whether United’s following Premier League fixture at home to Brighton and Hove Albion on Saturday will be affected.
On the Brentford postponement, the Premier League said: “The decision was taken following guidance from medical advisers due to the exceptional circumstances of an ongoing COVID-19 outbreak within Manchester United’s squad.
“First team operations at the club’s Carrington Training Complex were closed down today to help control the outbreak and minimise risk of further infection among players and staff.
“The league wishes a quick recovery to those players and staff with COVID-19. The postponed fixture will be rearranged in due course.”