The attack took place at a property on Thalia Street on Thursday afternoon (10 October), and involved the door being set on fire.
The PSNI are treating it as arson with a racially-motivated hate element.
Ms Nicholl has said: “This is an absolutely abhorrent incident, and I want to extend my sympathies to the family involved, including two young children who should never have been exposed to such hatred and cruelty. No child, or person in general, deserves that.
“Everyone deserves to feel safe in their homes, and respected and valued in their communities. South Belfast, and the city at large, is a welcoming place, and this attack is not who we are. Those responsible represent only themselves with such callous, violent behaviour, and they must be robustly condemned by all.
“We can only be thankful nobody was seriously injured, and I want to give my thanks to the NIFRS for their swift and effective response.
“I’d also encourage anyone who has any information that may be helpful to police in bringing those responsible to justice to please contact the PSNI, or report it anonymously via Crimestoppers.”