Sir Alex Ferguson Stand and Stretford End, containing around 20,000 spectators, at the stadium were evacuated before the home game against Bournemouth and sniffer dogs were brought in to search the stands.
Kick-off was delayed and shortly afterwards the match was abandoned on police advice.
The suspect package was found in the north-west corner of the stadium and a bomb disposal team carried out the controlled explosion. Fans in other stands initially had been allowed to stay inside the stadium.
Manchester United said in a statement: "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.
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"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."
The Premier League has announced it was looking to rearrange the match as soon as possible.
"The game will definitely need to be played but there are logistical issues that need to be resolved," a statement read.