Two stands – the Sir Alex Ferguson Stand and the Stretford End – were evacuated before the home game against Bournemouth and sniffer dogs brought in to search the stands.
Kick-off, due at 15:00 BST, was delayed and shortly afterwards the match was abandoned on police advice.
Security personnel are supervising fans exiting the stadium.
An “operation red code” alert was heard over the tannoy at 14:40 BST and the players who were warming up left the field.
The club announced: “Due to the discovery of a suspect package in the north-west quadrant of the ground, the match has been abandoned for today on police advice.
“People in the stadium are advised to remain in their seats while the forecourt is cleared of fans evacuated from the stadium. Further announcements will be made as soon as possible.”
Manchester United executive vice-chairman Ed Woodward spoke to Premier League chairman Richard Scudamore about the game being called off, BBC Sport’s football correspondent Phil McNulty said.
There is no indication yet as to when the game will be played.