The girl, Parichat Noopinit, had been in a coma at Trang Hospital since being electrocuted when she touched a Siam Commercial Bank (SCB) ATM at an Esso petrol station on Trang-Palian Road in Yan Ta Khao district.
The decision to turn off the respirator was reached after her heart stopped beating.
Parichat's grandfather Somchoke Khaokhong said that on the night of Aug 7 an adult had also received an electric shock from the same ATM, but had not been seriously injured.
The local electricity authority had been informed. His granddaughter was the next victim.
Local electricity officials had not fully examined the ATM and the power system at the petrol station, where the SCB ATM was sited alongside a Bangkok Bank ATM used by Parichat's much older sister to withdraw money at the same time.
Yan Ta Khao mayor Wuthichai Sunthornnont said he had heard reports of people receiving electric shocks at the ATM before the tragedy.
Yan Ta Khao police chief Pol Col Santhad Winson said police were still investigating. No charges had yet been laid.
The first priority was to help the young girl's family recover from the shock, he said. The SCB had accepted full responsibiity and was assisting the family, which was satisfied with the response, Pol Col Santhad said.
Trang police chief Pol Maj Gen Jeerawat Udomsud said the ATM was not connected to a transformer, but was wired directly into the electricity supply of the petrol station.
Refuelling and refilling petrol tanks at the station consumed a lot of power, he said. When such activities stop, the excess current could flow into nearby electrical devices, including the ATMs, and could well pass through anyone touching the metal body of the machine, Pol Maj Gen Jeerawat said.
In a statement on Friday, the SCB said it deeply regretted the incident and it was assisting the girl's family in many areas, including paying her medical and funeral costs.
The bank statement said it was concerned about ensuring pubic safety and was helping police and provincial electricity officials in the investigation.