The 64-year-old is survived by wife and two sons.
Mr Ahmed was rushed to a private hospital where he was declared brought dead, hospital sources said.
He was elected to the Lok Sabha from Uluberia constituency on a Trinamool Congress ticket.
He was elected to the West Bengal Assembly twice.
Prime Minister Narendra Modi and Chief Minister Mamata Banerjee condoled his death.
Saddened on the demise of LS MP & former Union Minister Shri Sultan Ahmed. My thoughts are with his family & supporters in this sad hour: PM— PMO India (@PMOIndia) September 4, 2017
Governor Keshari Nath Tripathi also expressed grief at the passing away of Ahmed.
Shocked and deeply saddened at the passing of Sultan Ahmed sitting @AITCOfficial LS MP & my long term colleague. Condolences to his family— Mamata Banerjee (@MamataOfficial) September 4, 2017