Revd Melvin Tinker, the vicar of St John Newland in Hull, made the comments while criticising a decision by a canon at York Minster to bless the city's Pride parade last weekend.
Mr Tinker made the comparison between homosexuality and paedophilia during an interview with Minster FM discussing the gay rights' march.
Diana Johnson, the MP for Kingston upon Hull North raised the issue in Parliament on Thursday, during questions to the Leader of the Commons Chris Grayling.
She said: "During the course of the same-sex marriage act, the Revd Tinker in Hull told me that if I supported it, he'd instruct his congregation not to vote for me. It might have something to do with the fact my majority went from 641 to 12,899. However, this weekend the Revd Tinker has equated homosexuality in the same category as paedophilia.
"Can we please have a debate in government time about the responsibilities of the established Church of England around community cohesion, and not inciting crimes of hate?"
Mr Grayling responded: "First of all, let's be absolutely clear. There is absolutely no connection whatsoever between homosexuality and paedophilia.
"Paedophilia is a crime, homosexuality is a reality of our society, it is something we have moved to support through same-sex marriage and through other changes in recent years. It is never acceptable to equate the two.
"Of course, as we were during the passage of the same-sex marriage act, it is important to be sensitive about these issues, particularly in relation to people with strong religious views, but there is never any justification for equating the two."
Speaker John Bercow said: "The misguided reverend is obviously rather a blinkered fellow, to put it mildly," to cheers from both sides of the House.
The Church of England said it would not be adding to the archbishop's statement.
