200 fans broke into their Old Trafford stadium to protest against the Glazer family's ownership of the club.
United fans got on to the pitch to protest and, after they were removed, some got back on to it later on.
The game was set to kick off at 16:30 BST but was put back on safety grounds.
"After the security breach at Old Trafford, we can confirm the Manchester United v Liverpool match will not kick off at 16:30 BST.
"The safety of everyone at Old Trafford is paramount. At present, there is no revised kick-off time.
We will update accordingly. All fans are believed to have been ejected from the ground and a sweep of the stadium is going to take place.
"We are being held while the stadium is cleared," said BBC 5 Live football reporter John Murray.
"Meetings are ongoing inside Old Trafford in one of the dressing rooms to decide what will happen next."
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