In a live discussion over the Christian run Ashers Bakery, Ms Nolan provoked controversy when she said: "If you went in somewhere and they said two days later 'we don't want to make your cake because of our beliefs' you'd just never go back to that shop and tell all your friends to boycott it.
"What if somebody walked in and said 'I want a cake with Islamic State on it and how I support it and how I support them killing our people' and because it's a business would they have to make that?"
The former pop star was reacting to the story in which the owners of Ashers were forced to pay £500 after refusing to bake a cake promoting gay marriage on the basis it went against its Christian beliefs.
A judge ruled they were guilty of discrimination but they are planning to appeal the verdict.
Ofcom says it received 140 complaints over Ms Nolan's comments, with some calling for her to be sacked, but it won't take any action.
In a statement it said: "We assessed a number of complaints that it was offensive for a panellist to compare same sex marriage to the terrorist group Isis (Islamic State), but won't be taking the matter forward for investigation.
"In our view, these unscripted comments during a live programme were unlikely to exceed the expectations of the audience and were justified by the context."