Published Tuesday, 08 May 2012
The 23-year-old had previously told his 50,000 followers that he "couldn't be happier to have been called up to represent my country".
While many of the responses congratulated McClean on making the team, some were much more menacing.
One 16-year-old schoolboy sent the Sunderland winger a message saying: "u deserve to be shot for that comment!! Your playing for Ireland and not the country you were born in (NI)".
The tweet has since been deleted, along with a few from other users.
The PSNI has said it doesn't discuss an individual's personal security, but a spokesman added that a formal complaint had not been received at this stage from McClean by police in Northern Ireland or in England.
McClean - who was capped seven times for Northern Ireland at Under-21s level, before being capped once at senior level for the Republic - initially hit back at his critics, but has since cancelled his Twitter account.
Foyle MLA Pat Ramsey has branded the threats "wrong and unfair".
He added: "One can certainly understand it, when they're going to European Championships, why someone would decide to opt for the Republic.
"It's a player's choice where they wish to go. People should honour and accept and respect that decision."
In February, McClean was praised by Republic boss Giovanni Tarpattoni, who said: "We regard him highly", while in March, he was rewarded for his efforts with club side Sunderland with a new three-year contract.
Later this month, the Republic will host Bosnia and Herzegovina in an international friendly and will go on to meet Hungary on 4 June in Budapest.
© UTV News