They fled from the central Phuket immigration office at 3am and only six have been recaptured by immigration authorities, police said.
The authorities were tight-lipped after the Rohingya, detained on charges of illegally entering the country, escaped, but reports were later confirmed by Phuket governor Maitree Inthusut, who ordered tightened security at the centre in Muang district.
Mr Maitree suspected that they were frustrated at being detained for so long at the centre. The group had been detained there since March.
Pol Maj Gen Chote Chawalwiwa, chief of Phuket police, alerted all police stations, public transport operators, local media and the public to keep an eye out for the escaped migrants. He said it was feared they would commit crimes and damage the image of the resort island.
It was the second escape of Muslim asylum seekers in Thailand in three days.
On Friday, 30 Rohingya detained in Sadao district of Songkhla province escaped from a police jail cell.
More than 1,700 asylum seekers from Myanmar who arrived in Thailand by boat early this year are being held in crowded detention centres, most of them in southern provinces.
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