Jim Wells MLA had apologised after saying that "facts show you certainly don't bring a child up in a homosexual relationship" at an election hustings.
The politician has always been open about being a devout Christian and has clashed with other MLAs in the past over abortion and gay men donating blood.
Elsewhere the Police Service of Northern Ireland has confirmed it is investigating alleged remarks he made to a lesbian couple whilst canvassing for votes.
Mr Wells confirmed he would stand down from the Stormont Executive on May 11th.
In a statement he said: "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.
"Some of the outbursts on social media have been particularly abusive and menacing in nature."
He said that his wife had been recovering from two strokes and major heart surgery.
"My focus will be on Grace and supporting my family. The events of the last week have taken place against the backdrop of a difficult period.
"On the issue of comments I have made which have attracted significant publicity, I have already said sorry for the offence caused and acknowledged that the comments were factually inaccurate.
"At no time did I set out to hurt or offend anyone and it has upset me greatly that the comments made have caused distress to some within our community."
DUP leader Peter Robinson accepted the resignation and said he respected Mr Wells' decision.
He said: "I would have wanted it to be otherwise but I respect Jim's decision. However, he is right to put his family first and I will fully support his decision.
"I place on record my thanks, and that of my party, for Jim's service and trust everyone will accept the stress and strain Jim has encountered over these past months and offer him and his family support and encouragement as Grace battles her illness."
Mr Wells will still be running as a Westminster candidate for South Down.
Other candidates running in South Down are Felicity Buchan (Conservative), Chris Hazzard (Sinn Fein), Harold McKee (UUP), Henry Reilly (Ukip), Margaret Ritchie (SDLP) and Martyn Todd (Alliance Party).