Jim Wells, a devout Christian, suggested a child was at more risk of abuse and neglect in a homosexual family.
The Police Service of Northern Ireland has confirmed it is looking into a complaint made following comments by the South Down MLA at an election husting event in Co Down on Thursday.
Mr Wells has apologised for his remarks and said he was under stress when he made the claims.
"I have listened to a recording of the relevant part of the debate," he said.
"I accept that one line of what I said caused offence and deep concern amongst members of the audience and beyond.
"I regret having wrongly made that remark about abuse and I'm sorry those words were uttered. The comment did not reflect my view nor that of my party.
"The last few weeks have been extremely difficult for me personally.
"I had just come from a hospital visit and my focus was not on the debate. Indeed, during the event I received several messages from the hospital."
Sinn Fein Deputy First Minister Martin McGuinness said Mr Wells' position was untenable and he must resign.
"Jim Wells' attack on the LGBT community was reprehensible and completely unacceptable from someone holding the position of health minister," he said.
Mr McGuinness added that the apology "rang hollow".
DUP leader Peter Robinson urged people to "give him a break" and said the politician had been under pressure and that his wife was seriously ill.
"I think anybody who looks at the comments will recognise that on a better day Jim would never have made such a comment.
"I think everybody knows the pressure he has been under the last couple of months with his wife being ill in hospital and trying to keep going a very significant department in the Executive.
"He has put out a very sincere and fulsome apology and I think people should give him a break because of the very special circumstances.
"He very rightly says it is neither his view or is it the Democratic Unionist Party's view. I again reiterate that today. That is not our view and nor will it ever be our view."