The match was scheduled to kick off at 16:30 BST on Sunday.
The Premier League in a Statement said, "This is a collective decision from the police, both clubs, the Premier League and local authorities," talks will now take place about re-arranging the game.
"The security and safety of everyone at Old Trafford remains of paramount importance," added the Premier League.
"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."
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