Mr Dick said the woman, who travelled to El Salvador, and the child, who recently returned from Samoa, were both recovering well.
The woman, aged in her 20s, became ill after returning to the Gold Coast from the South American country.
She tested positive to the mosquito-borne virus in January and was treated in hospital but was now recovering at home.
Mr Dick said the child was admitted to hospital on Thursday.
"The positive test came back today," he said.