The 23-year-old, who was born in Northern Ireland but has won 16 caps for the Republic of Ireland, was also targetted for his controversial switch of national allegiance.
Some of the messages posted on his Twitter page included: "Darron Gibson is on Twitter, a traitor to his country".
Another one said: "You are an abysmal excuse for a footballer. You're a one trick pony - a s(expletive) one at that. What Fergie sees in you I do not know..."
Gibson has been unable to establish himself as a first-team regular at Old Trafford since making his debut in a League Cup match in 2005.
He was also at the centre of a dispute over his international allegiance when he opted to play for the Republic of Ireland instead of Northern Ireland in 2007.
A number of United players have Twitter accounts with Rio Ferdinand a prolific 'tweeter' while star striker Wayne Rooney has attracted almost 200,000 followers after only joining the site on Saturday morning.
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