At approximately 12.50pm police received a report that a man had entered the shop and poured a flammable substance around the premises and set it alight.
The suspect then made off on foot along Donegall Street.
There were three people in the store at the time of this incident, none of whom were injured. However, they were all left very badly shaken.
The fire was extinguished by NIFRS.
Detective Sergeant Keith Wilson said: “It is believed this man purchased petrol from a filling station on Clifton Street before making his way to Donegall Street.
“Did you see him or do you have any information that could assist with our enquiries?
“If so, please call detectives at Musgrave Criminal Investigation Branch on the non-emergency number 101, quoting reference 540 23/02/18.
“Alternatively, information can also be provided to the independent charity Crimestoppers on 0800 555 111, which is 100% anonymous and gives people the power to speak up and stop crime.