The former Labour member is due to stand as a candidate for the All For Unity party in May’s elections.
Mr Galloway said he has left his home – and Scotland – after three separate death threats were made against him on Twitter.
He claimed the threats were written by a “Scottish Nationalist extremist”.
Police have confirmed they are investigating with Galloway praising a “prompt and determined response”.
Mr Galloway, who opposes Scottish independence, said he is suspending his election campaign “for a few days” until the police matter is resolved.
But he said he will still take part in The Scotsman’s online election hustings on Tuesday night “from a remote location”.
The hustings will start from 6:30pm with the livecast to focus on candidates from the South of Scotland list region.
Craig Hoy ( Scottish Conservatives) and Laura Moodie (Scottish Greens) are among the confirmed guests.
The All For Unity party launched last year and later issued a "Save Our Scotland" plea with people asked to vote against independence.
Mr Galloway earlier clashed with Justice Secretary Humza Yousaf after tweeting to the cabinet member: "You're not a Celt like me."
Mr Yousaf said voters will show George Galloway the “cat flap” at the May elections after the former MP posted a "race-baiting" tweet.
Mr Galloway said he held the “race-baiting” claim in contempt, given he was the father of five mixed race children.