The legislator of the Jokihat constituency in Araria district said he was asymptomatic.
Alam has been shifted to an isolation centre in the district, civil surgeon Dr MMP Singh said.
His sample was taken for testing to the Sadar Hospital on Tuesday and the report came on Wednesday evening.
Earlier, state minister Vinod Kumar Singh, along with his wife, and BJP MLA Jibesh Kumar Mishra had tested positive for COVID-19.
Singh, who is the Backward and Extremely Backward Class Welfare minister, was diagnosed with the disease on June 28 and sent to an isolation ward set up at a city hotel in Katihar district.
Mishra, who represents the Jale constituency of Darbhanga district, tested positive for the infection on June 22. He was admitted to AIIMS, Patna for treatment. COR AR RMS DPB