Measles were confirmed Sept. 7 in the child who flew to Wisconsin Aug. 24, the Milwaukee Journal Sentinel reported Thursday.
Two more cases have been confirmed in people apparently exposed to the refugee patient, the Centers for Disease Control and Prevention in Atlanta reported.
The CDC said another case has been confirmed in an unvaccinated 15-year-old Burmese refugee who flew from Malaysia to California the same day.
Three other unvaccinated refugee children who were on the same flight have also come down with confirmed cases of measles, the center said.
"Whether these three patients were exposed to measles in Malaysia or during travel to the United States is unclear," the CDC said.
To prevent further transmission of measles, refugee travel from Malaysia to the U.S. has been suspended, U.S. authorities said.
The CDC is recommending U.S.-bound refugees in Malaysia be vaccinated for measles, mumps and rubella, and have their travel to the U.S. postponed for 21 days after vaccination.