Craig Wallace, also known as Muhammad Mujahid Islam, 23, will appear at Hendon Magistrates’ Court in London tomorrow.
Wallace, of Teignmouth Road in Willesden Green, north London, was charged with the offence of malicious communications.
He was arrested at his home and remains in police custody until his court appearance.
Scotland Yard declined to name the MP, but said the politician does not represent a London constituency.
The charge comes after a number of MPs, many of them in the Labour Party, complained to police that they had received death threats after voting in favour of airstrikes on Islamic State in Syria.
Neil Coyle, the MP for Bermondsey and Old Southwark, said police had stationed extra officers outside his surgery after he received an apparent death threat on social media.
While Labour Rochdale MP Simon Danczuk has spoken out about receiving an apparent death threat on Facebook after he voted in favour of the military action.