Ian McCrea said most people in NI belong to denominations that hold the Pope to be "the Antichrist".
He said many Catholics would oppose the visit over clerical abuse scandals and Protestant opposition could be "detrimental to community relations".
Sinn Féin's Daithí McKay said the DUP should apologise for comments.
"Such comments are sheer lunacy and potential investors from abroad, especially mainly Catholic countries such as France, Spain and Italy, could be put off from investing here if they believed that the majority of people in the north opposed the visit of the Pope and saw him as the Antichrist," the North Antrim assembly member said.
Pope Benedict XVI is to travel to the UK next year for the first papal visit since 1982 and may include a visit to Northern Ireland.
SDLP Mid-Ulster MLA Patsy McGlone said Mr McCrea should apologise for his "deeply offensive comments".
"It is totally hypocritical at a time when the DUP are talking about building a shared future that one of their assembly members comes out with this utterly sectarian and abusive rant.
"This type of attitude only serves to create divisions and incite disrespect within our society," he said.
On his website Mr McCrea outlined his reasons why the Pope should not visit.
"I have been made aware, that should there be a visit from the Pope to Northern Ireland it will face the vent of Protestant opposition and therefore I believe that it would be detrimental to community relations and, on those grounds alone, I would urge the Pope of Rome not to come to Northern Ireland," he said.
The Evangelical Protestant Society has issued a statement backing Mr McCrea.
"As evangelical Protestants, we believe in civil and religious liberty for all, and we accept that a religious leader has the right to pay a pastoral visit to his flock," it said.
"But the pope is no ordinary religious leader, and his visit cannot be merely pastoral. Indeed, the planned visit to Great Britain will be the first state visit by a pope since the Reformation."
It was issued by Wallace Thompson, who the EPS website lists as being a former adviser to a DUP minister.
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SIC: BBC