Phasi Charoen police station, who were notified of the shooting at 3am, dispatched officers to investigate the incident at Saree Sauna & Spa on Ratchapruek Road.
The police said a fight involving the three broke out around 10.30pm on Tuesday and one of them reportedly decided to pull a gun and shoot the others, one in the neck and the other in the bottom.
A female Facebook user, who claimed to be a witness, posted a picture of the incident, explaining that the alleged gunman was Apirak Chat-arnon, who was previously invited by a government organisation to provide counsel on online gambling issues.
However, the police are checking footage from security cameras and collecting more evidence before they identify the offender.
The disputants have already begun legal proceedings against each other by reporting the incident to the police.