By Agence France-Presse
The Phoenix ran into trouble on Thursday afternoon, when it was hammered by five-metre (15-feet) high waves that had been whipped up by a storm.
The boat, which had left the popular snorkelling spot of Koh Racha to return to Phuket, was carrying 105 passengers, the majority Chinese tourists.
The body of one of the passengers, believed to be a Chinese holidaymaker, was pulled from the sea late Thursday and brought to shore, shortly before the search was called off for the night.
Helicopters, police and fishing boats were deployed early Friday as the rescue mission restarted.
"We will conduct air searches and send divers to check inside the sunken Phoenix boat," Noraphat Plothong said.
"Police investigators said most of the tourists were wearing life jackets," when the boat went down, he added.
Thailand is already in the global spotlight for a dramatic rescue mission in the north of the country, after 12 boys and their football coach were trapped in a cave complex.
Stunned survivors of the boat accident huddled in blankets on a Phuket pier late Thursday.
Some cried while others appeared dazed as they walked around still wearing their life vests.
"Eleven are injured, of these two are in serious condition," the governor added.
The Phoenix was among several boats that appeared to have ignored a severe weather warning in place since Wednesday to take tourists on day-trips to the islands that dot the seas off Phuket.
A Chinese consular official arrived at the operations centre in Phuket to monitor the rescue effort.
Several other vessels hit trouble late Thursday. Initial reports from officials said all of the passengers on those boats were rescued.
But as details dripped through overnight, governor Noraphat said two passengers were still unaccounted for from another stricken ship.
Phuket is a magnet for overseas visitors including Western sun-seekers and huge numbers of Chinese tourists who make up the bulk of the 35 million people expected to visit the kingdom this year.
Thailand has a poor health and safety record and accidents are common on its roads and busy waterways -- especially in tourist areas during the monsoon season which is now biting.