Hundreds of United fans made their way into the ground and onto the pitch in protest against the owners, the Glazer family, lighting flares ahead of kick-off.
The game, which was scheduled for a 4.30pm kick-off, was initially postponed indefinitely, but the decision was made to postpone the match on safety grounds.
In a statement, Manchester United said: "Following discussion between the Police, the Premier League, Trafford Council and the clubs, our match against Liverpool has been postponed due to safety and security considerations around the protest today.
"Discussions will now take place with the Premier League on a revised date for the fixture.
"Our fans are passionate about Manchester United, and we completely acknowledge the right to free expression and peaceful protest. "However, we regret the disruption to the team and actions which put other fans, staff, and the police in danger. We thank the police for their support and will assist them in any subsequent investigations."
A Premier League statement said: “This is a collective decision from the police, both clubs, the Premier League and local authorities.
“The security and safety of everyone at Old Trafford remains of paramount importance. We understand and respect the strength of feeling but condemn all acts of violence, criminal damage and trespass, especially given the associated COVID-19 breaches.
“Fans have many channels by which to make their views known, but the actions of a minority seen today have no justification.
“We sympathise with the police and stewards who had to deal with a dangerous situation that should have no place in football.
“The rearrangement of the fixture will be communicated in due course.
Supporters pre-planned after co-owner Joel Glazer's bungled attempt to join a European Super League.
A group of United fans broke into the club's Carrington training ground earlier this week, with manager Ole Gunnar Solskjaer and midfielder Nemanja Matic both speaking to the group of protesters at Carrington.
On Sunday, referee Michael Oliver, as well as former United captain Gary Neville, had their vehicles surrounded as they entered the stadium.
Those fans who gained access to Old Trafford did so via the Munich Tunnel after pushing down barriers, despite the attempts of security guards to prevent that happening.
Police cleared the stadium twice, with fans finding their way back in relatively unchallenged after the first wave of protesters, before the immediate vicinity around Old Trafford was then emptied of supporters.
However, the decision was then made to call off the match.