The woman, 24, stopped breathing during a procedure at a clinic in Bangkok on Thursday, an official said.
A doctor, Sompob Sansiri, has been charged with recklessly causing the woman's death and bailed, police said.
The Foreign Office said it had been informed of the death and was "ready to provide consular assistance".
The patient, who has not been named, was having minor corrective surgery to her back after a previous operation, officers said.
The director general of Thailand's health service support department, Boonruang Triruangworawat, said attempts had been made to revive the woman when she stopped breathing.
She was under anaesthesia when she died, Thai police said.
The Thai Ministry of Health said it would file a charge of operating an unlicensed clinic because the facility was not licensed to operate at night.
The SP Clinic has been shut down for 60 days while the death is investigated.
A British woman understood to have gone to Thailand for cosmetic surgery has died during an operation, Thai officials have said.