The Blur frontman said he feared Mr Rees-Mogg could topple Theresa May as Britain fast approaches the Brexit deadline of 29 March.
Albarn, 51, said two years ago he had vowed to leave the UK if the MP for North East Somerset ever took power.
Reflecting on reports of an attempted coup by Leave-backing MPs over the weekend, Albarn said: “That terrifies me. The fact that Jacob Rees-Mogg was at Chequers [the PM’s country house] this weekend.
“Jacob Rees-Mogg, prime minister of the UK, or even in the Cabinet, is a really terrifying proposition for all of us.
“I said two years ago that if he came properly into power I would leave the country. I’m serious.
“He’s too right. I don’t want this country to be inhabited by that level of right extremism.
“It’s extremism. There’s no place for extremism. It’s troubling.”
Albarn, who is about to embark on a tour of intimate venues with his band The Good, The Bad and The Queen, said views held by Brexiteer MPs were not representative of the country.
He said: “It might resonate in north Somerset, but it means nothing in Blackpool.
“It was one of the first things that blew my mind about the referendum, was that people were getting into bed who had nothing in common and had no intention of helping each other.”
Albarn, who backs a second referendum on leaving the European Union, marched for a final say on Brexit alongside a reported one million others during Saturday’s Put it to the People event in London.
The musician, who writes and performs as the virtual rock band Gorillaz, also marched against the Iraq War in 2003.
Comparing the two, he said: “I was right at the front of the first one and I was pretty much at the back of this one. A very different dynamic obviously.
“It was very civilised. It was articulate. People had just really gone to town with their placards. Some of them were hilarious. It wasn’t a negative thing at all.
“I just think it’s tragic that we have created this division in this country. That’s where the sadness on the record comes from.”