The 23-year-old Derry-born Sunderland winger made the move after he was sent a message saying he "deserved to be shot" for opting to play for the Republic rather than Northern Ireland.
Another user told McClean he would "make sure you get shot when you set foot back into god's country."
The Football Association of Ireland expressed disappointment with the threats aimed at the player, and backed his decision to withdraw from the social network site. "It's a pity it has come to this, but it is maybe in his best interests in the short term," a spokesman said.
McClean was the subject of abuse earlier this season when he announced his decision to play for the Republic, which is allowed under the terms of the Good Friday Agreement.
Northumbria Police confirmed they have received no complaint about the threat, while a spokesman for the Police Service of Northern Ireland said: "We do not discuss the security of any individual.
"However, if we receive information that a person's life may be at risk, we will inform them accordingly. We never ignore anything which may put an individual at risk."
McClean is currently on Wearside preparing for Sunday's final Barclays Premier League fixture of the season against Manchester United.
Black Cats chief executive Margaret Byrne said: "Any incidents of this nature are treated with the utmost seriousness and the club is looking into this matter carefully."
McClean was also inundated with messages of support from both sides of the border following his inclusion on Monday in Giovanni Trapattoni's 23-man squad for the finals in Poland and Ukraine.
He has just one senior cap to his name to date, and that from an appearance as a substitute in a friendly against the Czech Republic in February. His emergence from the bench was greeted by rapturous applause by fans at the Aviva Stadium, and his form for Sunderland since has earned him a seat on the plane.