The incident happened at about 2 a.m. at Saied Deli on East 125th Street.
According to investigators, the suspect was observed by staff attempting to walk into the back of the store to steal beer.
He was escorted outside as he was insulting and threatening an employee.
After the store staff closed the front door and switched operation to the front window, the suspect responded by pouring flammable liquid into the window and igniting it, police say.
The employees were able to extinguish the fire and no one was hurt.
The suspect fled eastbound on East 125th Street toward Lexington Avenue, authorities say.
He is described as 23-35 years old, 6'2", slim build, last seen wearing a black hooded sweatshirt, tan pants, black sneakers and black and white Brooklyn Net knit hat.
Anyone with information is asked to call Crime Stoppers at 1-800-577-TIPS (8477). The public can also submit tips by logging onto the Crime Stoppers website at http://WWW.NYPDCRIMESTOPPERS.COM or by texting their tips to 274637 (CRIMES) then enter TIP577.