Jim Wells is the first Northern Ireland minister to quit after an outcry over alleged homophobic remarks, the region's devolved Assembly has been told.
Sinn Fein said it was a mark of progress but the DUP appealed for critics not to use "lynch mob" tactics against the embattled health minister.
Mr Wells confirmed he would be standing down on May 11 to care for his seriously ill wife.
The announcement came hours before the DUP vetoed an attempt to legalise gay marriage.
Mr Wells had been facing calls to resign since the release of video footage in which he said the "facts show you certainly don't bring a child up in a homosexual relationship".
An alleged verbal altercation with a lesbian couple during an election canvass in his South Down constituency added further pressure.
Sinn Fein MLA Daithi McKay said: "This is the first time that a politician has been forced to resign in the north because of the strength of public opinion against homophobic remarks.
"I think that is a big change for us as a society, particularly for us in the north of this island.
"I believe the public recognised that it's wrong, simply wrong, to speak about gay people in that way."
In a statement Mr Wells claimed he had been subjected to menacing attacks on social media.
"I am deeply saddened that some of those who represent a different viewpoint from me have attacked my family and me in a deeply personal, nasty and, in some cases, threatening way," he said.
"Some of the outbursts on social media have been particularly abusive and menacing in nature."
The DUP's stance on LGBT issues, such as its opposition to gay marriage, has been subject to greater scrutiny beyond Northern Ireland during the election campaign, given the party's potentially important role in the event of a hung parliament.
Last week Liberal Democrat leader Nick Clegg said the furore was an indication of the "truly backward-looking views from the DUP", but he would not rule out governing alongside the party after the General Election.
DUP leader Peter Robinson said Mr Wells should not be subjected to a "lynch mob" by critics.
He said: "I do ask people that they should not take on the characteristic of a lynch mob about these matters.
"He has apologised, he has accepted that the facts were inaccurate as he recalled them.
"I immediately went out to indicate that they were not the views of the party, nor would they ever be. That is the clearest direction I can make."
The DUP used a blocking mechanism to stop same-sex marriage becoming legal in Northern Ireland.
It was the fourth time the divisive issue was debated on the floor of Parliament Buildings.
Mr Robinson said his party would not be recognising the marriage of a gay couple.
He said: "The institution of marriage that many of us recognise is that it is an ordnance handed down from God for the appropriation of children, to ensure that a man and a woman can get married.
"If there is a same-sex relationship that is catered for within the scope of the existing law by way of a civil partnership, I cannot understand why you have to redesign the God-given term of marriage in order to ensure that it caters for something that already exists under the law by way of civil partnership."
John O'Doherty, director of the Rainbow Project, which supports gay, lesbian and transgender people in Northern Ireland, said: "Northern Ireland's acceptance of LGBT people has grown immeasurably over the last 15 years.
"We expect political leaders and especially government ministers to keep pace with public acceptance, uphold their obligations under the ministerial code and work with our community to create a society where all are treated with dignity and respect.
"In recent months the DUP and others who share their views have been calling for dignity and respect for differing views between some Christians and the LGBT community. It is time for the DUP to show leadership on these issues and show dignity and respect for our community and issues which impact negatively on the health and well-being of too many."
The Church of Ireland group Changing Attitude Ireland (CAI) has also called on Northern Ireland politicians to "dismantle the architecture of homophobia".
CAI spokesman Canon Charles Kenny said: "It is time for conservative Christians in Northern Ireland to cease personal attacks on same-sex couples."
Amnesty International accused some politicians of being out-of-touch with public opinion.