Tens of thousands of fans were ordered from the 75,600 capacity stadium when the alert was sounded about 20 minutes before the scheduled 1400 GMT kickoff.
The game "has been abandoned, fans are leaving the ground. Please avoid the area if possible", Manchester police said on their Twitter account.
United confirmed that a security alert caused the abrupt cancellation.
"Due to the discovery of a suspect package in the North-West Quadrant of the ground, the match with Bournemouth has been abandoned today on police advice," a United spokesman said in a statement.
Half of the stands at Old Trafford were evacuated. United said the suspect package had been discovered in the Stretford End stand.
Public address announcements instructed supporters in the South and East Stands -- including travelling Bournemouth fans -- to remain in their seats before the game was called off.
It is the second time in less than a week that Manchester United have been involved in a security alert.
Their game at West Ham United on Tuesday was delayed after their team bus was attacked by fans.
There was no initial indication of the seriousness of the incident but by the scheduled 3:00pm kick-off (1400 GMT), stewards outside the ground were telling supporters that the game had been abandoned and, within minutes, the decision was confirmed by police.
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