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..."