Kusak Kukiatkul, Phuket's public health chief, said an eight-year-old and a nine-year-old from Myanmar had tested positive at the end of the first week in Phuket.
He said the two children were being treated at a hospital, adding that five members of their family must be quarantined for 14 days.
"Disease investigation officers are currently looking into the timeline of two new Covid-19 cases during seven days in Phuket," he said.
He also asked people in Phuket to have faith in disease investigation officers and not panic.
Earlier, a United Arab Emirates national on July 7 became the first person travelling under the Phuket Sandbox scheme to test positive for Covid-19.