The Third Naval Area Command, which oversees Thai territories on the Andaman Sea, sent the protest after an urgent meeting of the Thai-Myanmar General Border Committee (GBC) to discuss the incident.
The crew of 14 jumped into the sea after the fishing vessel came under fire, navy spokesman Niphan Chamachot told the Thai News Agency.
The crew was saved by a Thai navy ship stationed nearby, but the vessel has now been impounded and its captain held in custody, Capt Niphan said.
The skipper, identified as Kayu Suksawat, is safe.
Capt Niphan said the incident comes despite a warming in ties between Bangkok and Nay Pyi Taw - especially in light of the recent visit of Myanmar's Supreme Commander Snr Gen Min Aung Hlaing early last week. He he met Prime Minister and Defence Minister Yingluck Shinawatra and Thai military top brass.
"The situation is far from tense," he said, adding such misunderstandings can sometimes occur on the overlapping border.
The incident took place near Ko Khom, an island near a disputed border. It is about two nautical miles off Ko Chang, the largest island off Ranong province.
The Thai fishing boat, a trawler named Montri Thawisin 3, came under fire from Myanmar navy officers as it sailed a short distance from Ko Kom early Saturday, according to the initial investigation.
The boat is now under Myanmar officers' control and is docked at Kawthaung at the southern tip of Myanmar, according to a media report.
Thai authorities and the boat owner have asked Myanmar officers to return the boat but to no avail.
The boat belongs to Surin Losong, who is also the chairman of Ranong Fishermen's Association. Mr Surin said he was contacted by Mr Kayu about 1.30am.
Mr Kayu said his boat was attacked by Myanmar warship PGM Number 426.
Mr Kayu claimed the ship encroached on Thai territory, Mr Surin said.
The skipper decided to have his crew, comprising Myanmar nationals, jump into the sea to escape the attack, he said.
Mr Surin said he later tried to ask Thai navy officers stationed on Ko Chang to help Mr Kayu. They allegedly said they could do nothing because they needed to wait for orders from their commander.
"That's what I didn't understand," Mr Surin said, asking why the Thai navy did not respond to an attack allegedly carried out in Thai territory.
He said local fishermen would do what they could to help Mr Kayu, following their disappointment with the help offered by Thai authorities.
He claimed Montri Thawisin 3 was the third of his boats to be attacked and seized in Thai territory this year. Other boat owners have encountered similar incidents, he said.
A marine police officer in Ranong Saturday warned Thai fishermen against sailing near the disputed area.
The Marine Police Division and state agencies should warn the fishermen about the territorial conflict between Thailand and Myanmar, Pol Lt Col Nirat Chuaichit, the province's marine police inspector said.
He said fishermen must act with more caution to avoid being arrested by Myanmar officers.
Manasvi Srisodapol, the Foreign Ministry spokesman, said the ministry has yet to receive any official information regarding the incident.
However, he has unofficially contacted a coordinator at the Thai-Myanmar Township Border Committee for Ranong and Kawthaung.
Mr Manasvi said he could not comment further until the Foreign Ministry had received official information from the state agencies involved.