Shadow leader of the House, Chris Bryant, who previously worked as an Anglican priest, is unhappy at what he says is Mr Fury's homophobic attitude.
Fury, a committed Christian, has been criticised for his traditional views about sexuality.
Mr Bryant, who is gay himself, told MPs that, while Fury has been nominated for the BBC Sports Personality of the Year award, he hopes he does not win.
The Gypsy King, & the heavyweight champion of the world, will not be silenced I'll always speak my mind, Like it or lump it, in Jesus name.
— Gypsy King (@Tyson_Fury) December 3, 2015
Mr Bryant said MPs may well have been aware of the boxer's comments.
"There are only three things, he has said, that need to be accomplished before the devil comes home," the shadow leader said.
"One of them is homosexuality being legal in countries, one of them is abortion and the other one is paedophilia.
"Leaving aside the bizarre rather heterodox theology, this equates homosexuality with paedophilia."
Mr Bryant said that is "profoundly offensive" and is the "kind of language that leads to more young people committing suicide".
"I gather Mr Fury has subsequently said that some of his best friends are gay," he said.
"So can I suggest that we invite him to Parliament sometime in the near future because frankly I am quite happy to go head to head with him."