Police said the group bored through two small holes into the wall of the centre in Sadao, near Thailand's southernmost border, using blankets to climb out as heavy rains masked their flight.
The group have been held since in 2014 despite their claims to be Turkish citizens.
Turkey shares ethnic links with the Uighurs and accepts those who flee from China, where the Muslim minority are persecuted and subject to tight controls on movement.
"Twenty are still on the run but... they don't have food and cannot communicate with villagers," Immigration Police spokesman Cherngron Rimpadee told AFP.
"They are likely to aim for Malaysia. We believe they will be caught soon," he said, adding border patrols have been beefed up.
Six Thai immigration officers have been transferred pending an investigation into the breakout.
In July 2015 over 100 Uighurs, who were initially detained with the group of escapees, were handed over to Chinese authorities and deported against their will.
Two Uighur-origin men are facing trial for the bombing, sparking speculation the attack may have been in revenge for the forced deportation.
Uighurs often claim Turkish citizenship to avoid return to China.
Thailand does not grant asylum to refugees but has said Uighurs can remain in Thai custody until their citizenship is established.
Thai Immigration Police says 61 Uighurs remain in detention across the country.
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