He wrote on Twitter: “A threat against my life has just been posted on Twitter by a Scottish Nationalist extremist.”
He later added: “Thanks to all well wishers. We have left home - indeed left Scotland - until the Police have apprehended the man who made the threat.
"Family safe. Thanks for your concern.”
A spokesperson for the police said: “Police Scotland have received a complaint of an offensive communication which is being investigated and enquiries are ongoing.”
Mr Galloway is standing as part of the All for Unity party in May’s elections.
He launched the party last year, later issuing a "Save Our Scotland" plea as he asked people to vote against independence.
He is hoping to win a seat in the South of Scotland region.