The game's rescheduling follows the Premier League's announcement on Monday of a record-high 42 new positive Covid-19 tests between Dec 6 and Dec 12 -- more than triple the previous week's total of 12 and eclipsing the largest recorded weekly total of 40 in January.
A statement from the league announced a return to its "emergency measures," which include protocols on wearing face coverings indoors, observing social distancing, limiting treatment time, as well as an increase in lateral flow and PCR testing of players and staff.
"We will continue to work closely with the Government, local authorities and supporter groups, while being responsive to any future changes to national or local guidance," the Premier League said.
Brentford's scheduled hosting of United had been cast into doubt on Monday afternoon after the visitors announced the 24-hour closure of their Carrington Training Complex due to a number of positive Covid-19 cases among first team staff and players.
A statement from United said that those who tested positive were isolating and that the club were in discussions with the Premier League over the continuation of the Brentford fixture.
The league later confirmed that the game had been postponed "following guidance from medical advisers due to the exceptional circumstances" of United's Covid-19 outbreak and would be rearranged at a later date.
Both clubs released statements regarding the postponement recognizing the "inconvenience" caused to fans, with United confirming that they had requested the game's rearrangement.
"We appreciate that there will be many fans who will be inconvenienced with the fixture postponement and we apologize for the disruption, which was out of our control," Brentford's statement read.
"But we respect the Premier League's decision and acknowledge that the health and safety of both clubs' players and staff must always come first."
'Now, we are a bit scared'
It marks the second postponement in as many days as rising Covid-19 cases threaten to derail a hectic winter period in English football.
Sunday's fixture between Brighton and Tottenham Hotspur was similarly postponed last Thursday due to a Covid-19 outbreak in the visiting camp -- with Spurs manager Antonio Conte announcing positive cases among eight players and five staff members.
Spurs' UEFA Europa Conference League fixture against Stade Rennais on Thursday did not take place due to the club's high number of cases, with a statement from UEFA saying that "despite all efforts, a solution that could work for both clubs could not be found."
A statement from Spurs read: "We should like to apologize to everyone at Stade Rennais and Brighton & Hove Albion and to both their supporters and ours for any inconvenience caused.
"We should also like to thank both clubs for their understanding during these challenging times."
Conte confirmed the extent of the outbreak on Thursday, admitting that he was "very upset" as a result of the "strange and incredible" situation.
"It's contagious and there is a big infection. Now, we are a bit scared because tomorrow we don't know what will happen," Conte added.
Rodgers expects Spurs game to continue
Spurs are set to face a club similarly navigating a number of positive Covid-19 cases -- Leicester City -- on Thursday, with Leicester manager Brendan Rodgers expecting the game to go ahead.
Rodgers was without several players for his side's matches against Napoli and Newcastle over the last week.
"I can't give the number of Covid cases," Rodgers said after his side's 4-0 rout of Newcastle.
"It's medical and something I don't need to declare to you, but we have a host of players out, a mixture of Covid and of course players that aren't well, so that's as much as I can say.
"I've not heard anything that the Spurs game is not on, and obviously with the European decision as well with Tottenham not being able to play, I suspect the game would go ahead. We haven't been told anything otherwise."
Gerrard on signing vaccinated players
Though not to the same extent as Conte, Aston Villa manager Steven Gerrard is another Premier League boss wrestling with selection issues caused by Covid.
Speaking yesterday to reporters ahead of his side's trip to Norwich tonight, Gerrard confirmed "a couple" of positive cases among players.
Gerrard also revealed that the vaccination status of potential signings would be considered as part of the club's transfer strategy.
"We look at everything, so I'm sure it will come up," Gerrard said.
"I don't think it's right for me to comment on if I would or wouldn't in that situation, but it would certainly come into conversations in the background."
'The doctors suggest that they have to do it'
Meanwhile, Manchester City manager Pep Guardiola has said that players and staff have been encouraged to get the Covid-19 booster jab by the club's medical team, referencing the outbreaks at Spurs and Leicester.
On Sunday, the United Kingdom increased its Covid-19 alert level and accelerated its rollout of booster jabs in response, with Prime Minister Boris Johnson setting a new target of offering all adults a third shot by the end of December.
"Absolutely, the doctors suggest that they have to do it [get the booster]," Guardiola told reporters on Monday ahead of City's game against Leeds tonight.
"I am not concerned because they might cancel the Premier League, I am concerned because the virus is here and people suffer. You have seen it at Spurs, Leicester -- there are many.
"Now, at Christmas time, the tendency is to organize parties and go out, it's normal. But the virus is still here, the old and the new variant."