Connaire McGreevy's sister Ciara died last month. He had changed his profile picture on Facebook to an image of her.
Mr Wells asked Mr McGreevy on Facebook: "Who is that drop dead gorgeous young women (sic) on your Facebook site?"
"Is she your daughter or a promotional model you have hired to advertise your company?"
He replied: "Eh, Jim Wells, that is my sister who passed away a month today."
Mr Wells, a former Northern Ireland health minister, responded to say he would delete the post. It has since been deleted.
A DUP spokesman said: "Jim has known Connaire a long time but was unaware that his sister had died.
"It was a light-hearted comment and when Connaire called him to explain he apologised.
"He didn't want to cause offence. It was certainly not what he set out to do."
Jim Wells has apologised for making a "light-hearted comment" on social media about the dead sister of a former SDLP councillor, the DUP has said.