The footage which emerged over the weekend was taken at the Local Women Business Awards at a Belfast hotel.
In the video, the woman poses for a selfie with the former first minister before starting to chant.
As as teenager in 1988, the IRA set off a bomb on the school bus she was on.
"For Arlene and for victims across Northern Ireland who have suffered so much," he said.
"For someone to think it appropriate to come up to them to chant in their face the name of the organisation that tried to murder her father, the name of the organisation that tried to blow up her school bus is frankly beyond the pale."
He praised Dame Arlene and said the former DUP leader had expressed a desire to explain to the woman how the chant had affected her.
"Why do this? Can we not disagree decently? It serves no cause or community," he added.
Ulster Unionist Party assembly member Robbie Butler said: "What probably saddens and sickens me most is that the majority of those responsible for causing offence and deliberately causing hurt is that almost none of them grew up through the evil dark destructive days they glorify."