Sub-divisional Magistrate, Sarvesh Kumar Yadav, said the reports of the two came on Monday night.
Besides the two, a pharmacist at the district hospital also tested positive for COVID-19.
The Ballia district administration has declared a lockdown in urban areas of the district till July 10.
In another development, a case has been registered against a COVID-19 patient, who had fled from a hospital in the district on Monday, Additional Superintendent of Police, Sanjay Yadav, said.
The patient was admitted to the hospital on July 2. CORR NAV DV DV