This is the fourth top flight clash to be called off this week with Man United's trip to Brentford, originally scheduled for December 14, one of the matches.
The Daily Telegraph reports that Red Devils interim boss Ralf Rangnick had just nine available players from the first-team squad available for Brentford and that number has since gone down to seven.
However, the Premier League outlined its intention for other fixtures to go ahead as scheduled this weekend where safe.
That's despite growing calls for all Premier League games to be postponed until after Christmas, with Brentford manager Thomas Frank and talkSPORT pundit Simon Jordan among those using the top flight to act.
A statement read on Thursday: "Manchester United's fixture against Brighton and Hove Albion this weekend has been postponed by the Premier League Board today.
"It is with regret that this is the fourth Premier League fixture to have been postponed in the past week.
"While recognising a number of clubs are experiencing COVID-19 outbreaks, it is the League's intention to continue its current fixture schedule where safely possible. The health and wellbeing of all concerned remains our priority.
"Regarding Manchester United's game on Saturday, the club continues to have an ongoing COVID-19 outbreak within their squad, which has left them unable to field a team for the match at Old Trafford.
"A significant number of COVID-19 cases led to their game against Brentford FC being called off earlier this week, and today additional positive tests have been confirmed.
"The Board assesses applications to postpone matches on a case-by-case basis, based on existing rules and COVID-19 postponement guidance issued to all clubs. It will assess a number of factors, including the ability of a club to field a team; the status, severity and potential impact of the COVID-19 outbreak at the club; and the ability of the players to safely prepare for and play the match.
T"he Board must also consider the wider risks to the opposition and other people the club may come into contact with.
"In light of the recent rise in COVID-19 cases across the country, the Premier League has reintroduced Emergency Measures. These include protocols such as more frequent testing, wearing face coverings while indoors, observing social distancing and limiting treatment time."
"Regarding Manchester United's game on Saturday, the club continues to have an ongoing COVID-19 outbreak within their squad, which has left them unable to field a team for the match at Old Trafford.
"A significant number of COVID-19 cases led to their game against Brentford FC being called off earlier this week, and today additional positive tests have been confirmed.
"The board assesses applications to postpone matches on a case-by-case basis, based on existing rules and COVID-19 postponement guidance issued to all clubs. It will assess a number of factors, including the ability of a club to field a team; the status, severity and potential impact of the COVID-19 outbreak at the club; and the ability of the players to safely prepare for and play the match.
"The board must also consider the wider risks to the opposition and other people the club may come into contact with.
"In light of the recent rise in COVID-19 cases across the country, the Premier League has reintroduced Emergency Measures. These include protocols such as more frequent testing, wearing face coverings while indoors, observing social distancing and limiting treatment time."
But this isn't enough in the eyes of Brentford boss Thomas Frank, who believes a brief suspension of all fixtures is required for the Premier League to effectively combat the Omicron variant.
There's huge doubt over Brentford's trip to Southampton going ahead on Saturday with Frank revealing his club currently has 14 COVID cases.
"We think we should postpone the full round of Premier League games this weekend," he said on Thursday morning.
"COVID cases are going through the roof at all Premier League clubs, everyone is dealing with it and having problems.
"To postpone this round and also the Carabao Cup round would give everyone a week at least, or four or five days to clean and do everything at the training ground so everything is clean and you break the chain."
"We fully respect that we want to play and it is important football keeps going, and this way we can make sure Boxing Day keeps going, I'm 100 per cent sure of that," added Frank.
"This Omicron variant is running like wildfire around the world and I think we need to do all we can to protect and avoid it. I think we can do a lot by closing down training grounds for three, four or five days, and then we can go again."