The 35-year-old, named by American media outlets as Nemariq Alhinai from Glasgow, was wearing a hijab and looking through the windows of posh clothes shop Valentinos at 8.58pm on Saturday night.
Nemariq, thought to be a dentist working in Hamilton, South Lanarksire, was walking in Midtown Manhattan’s Fifth Avenue when she felt something warm on her left arm and noticed her blouse was on fire.
She patted out the flames which left a coin sized hole in her top and saw a man standing next to her with a lighter in his hand.
She refused medical attention at the scene.
There have not been any arrests yet but the New York Police Department have released footage of their prime suspect walking eastbound on nearby East 54 Street.
VIDEO: This is the man who set a Scottish dentist on fire as she browsed a clothes shop window