The boy and girl, aged 10 and 11, had just returned from a trip to another province and are now recovering well in hospital.
Tambon San Sai Administrative Organisation has declared the 100-metre radius around the infected children's home as a disease-control zone.
“Over the next 14 days, we will seriously eradicate mosquito-breeding grounds and spray the area with mosquito-killing agents," the organisation's chief Natee Damrong said yesterday.
Spread by mosquitoes, Zika usually causes mild symptoms such as fever, rash, joint pain and conjunctivitis, but in severe cases it may cause brain damage or even death.
The disease is of a particular threat to pregnant woman as it has been linked with microcephaly, a condition associated with incomplete brain development.
The World Health Organisation declared Zika a "public health emergency of international concern" on February 1 after a spike in cases of microcephaly and Guillain-Barr้ Syndrome.
As of June 15, as many as 60 countries and territories report continuing mosquito-borne transmission of the disease.