The incident took place late on Monday night, when a blaze was discovered at the premises of a Turkish barbers in the town.
Neil Kelly said: “It is extremely distressing that a local business has been targeted in such a way. Besides the fact the owners will have to pick up the pieces after the full extent of the damage is determined, somebody could have been seriously injured or even killed in this attack.
“Thankfully on this occasion no-one was injured, but we must do all we can to protect people and retailers locally. Antrim is a welcoming place for all and we must stand together to ensure it stays that way.
“I wholeheartedly condemn this attack and would urge anyone with information to contact the PSNI as soon as possible.”