Tattoo artist Marcus Kuhn said he set up the shop using his life savings and has no money left to rebuild his studio.
Police said the fire began at about 03:15 BST on Wednesday in Cork Place.
"I'm gutted as we don't have insurance yet as we have been open for 11 days and had been waiting for the insurance to come through," Mr Kuhn said.
"I was told by police that somebody poured petrol through the front door, smashed the windows, poured more petrol into the shop and set it on fire."
Mr Kuhn said he was told by police the fire burned for about 45 minutes before it was reported.
The tattoo artist had recently returned to the UK after 32 years in the States due to his father being ill.
Mr Kuhn, who had been part of the world-famous Fun City in New York, said he had spent about Â£15,000 on the Bath parlour.
"I built it all myself, put in new hospital floors, re-plastered the walls, and now the windows are destroyed, the doors are destroyed, most of the equipment is destroyed," he said.
"I'm a very spiritual and positive person... I'm not going to be brought down by this, but I am going to try and get some help from the community about this because I really am at the end of my rope."
A tattoo parlour in Bath has been damaged in an apparent arson attack 11 days after opening.