Haque was a member of the East Pakistan Chhatra League Central Working Committee. He fought in the Bangladesh Liberation war in 1971 and was part of the Mukti Bahini. From 1973 to 1986, he was elected Upazila chairman three times and four times municipal mayor. He was elected to the parliament from Gazipur-1 in 2008. He was elected unopposed from the same constituency in 2014. He acted as the religious minister of Bangladesh from 2018 to 2019. In 2019, he was appointed the Minister for Liberation War Affairs.