Paramedics were called in at 3am as a precaution when police at Takuatung Police Station became aware of the escape attempt.
Details of how the escape was prevented have yet to emerge. Takuatung is in Phang Nga province, between Thai Muang and Khao Lak.
The Rohingya were among 261 detainees transferred from Phang Nga Immigration HQ to small surrounding police stations after a protest last week.
Thailand continues to struggle to find a solution to the issue of what it should do with about 1700 Rohingya apprehended in boats and ''rescued'' from traffickers' camps between January and March.
The men in Takuatung were among more than 100 Rohingya who landed on an island off Phuket on March 23. They had previously spent 40 days as detainees in the Indian protectorate of the Andaman and Nicobar islands.
Another 21 Rohingya remain on the loose after escaping from Phuket Immigration cells at the weekend. Fifteen have so far been recaptured.
No answers appears to be in sight to the Rohingya issue, either in dealing with the boatpeople now being held in Thailand or the broader dilemma of Burma (Myanmar) solving the inhumane persecution that continues within its borders.
A self-imposed six-month deadline for Thailand to determine the status and the future of its Rohingya detainees passed without a decision last month.
Immigration centre protests and escape bids have followed and are unlikely to end until the Rohingya - being held without charges being laid - resume their interrupted journey south to seek sanctuary in Malaysia.
It's believed that Thai military authorities support holding the Rohingya indefinitely to frighten others and prevent more Rohingya landing in Thailand when the safe ''sailing season'' resumes in October.
This week, a Phuket representative of the Army's Internal Operations Security Command contacted a Phuketwan reporter at an unrelated meeting at Phuket Provincial Hall in Phuket City and criticised Phuketwan for its coverage.
Accusations continue to be made by international news agencies and on independent television channels that renegade elements in Thailand's military have been involved in the human trafficking of Rohingya.
Villagers along the Andaman Sea coast and Rohingya who have fled to Malaysia, interviewed by international news outlets, have confirmed the renegade military involvement.
With concern growing about Burma's persecution of its stateless Rohingya population, the date for the shamelessly bigotted nation to take over the chair of the region's most important group, the Association of Southeast Asian Nations, in 2014 draws closer.
Critics of Burma's behavior in repressing its Muslim Rohingya population rather than granting them citizenship have predicted that if left unresolved by Burma, the issue will destabilise security in all neighboring countries.