He was suffering from cancer and had come back from the US in October after treatment at the Memorial Sloan Kettering Cancer Centre, New York.
Kumar, 59, is survived by wife and two daughters.
He breathed his last around 4 am, party spokesman Prakash told PTI.
Kumar’s wife Tejaswini and his two daughters were with him when he passed away, he said.
Kumar was a BJP MP from south Bengaluru constituency.
President Ram Nath Kovind, Prime Minister Narendra Modi, Congress President Rahul Gandhi and several political leaders Monday condoled the demise of Union Parliamentary Affairs Minister Ananth Kumar.
Kumar, 59, died at a private hospital in Bengaluru in the early hours of Monday after battling lung cancer for several months, hospital authorities said.
Expressing his condolences, Kovind said the death of Kumar was a tragic loss to public life in the country.
“Sad to hear of the passing of Union minister and veteran parliamentarian Shri H.N. Ananth Kumar. This is a tragic loss to public life in our country and particularly for the people of Karnataka. My condolences to his family, colleagues and countless associates,” he tweeted.
The Prime Minister said he was extremely saddened by the passing away of “my valued colleague and friend” and described him as a remarkable leader, who entered public life at a young age and went on to serve society with utmost diligence and compassion.
He will always be remembered for his good work, Modi said in a tweet.
Gandhi also offered condolences to Kumar’s family and prayed for peace to the departed soul.
“I’m sorry to hear about the passing of Union Minister, Shri Ananth Kumar ji, in Bengaluru, earlier this morning. My condolences to his family & friends. May his soul rest in peace. Om Shanti,” he tweeted.
BJP president Amit Shah said Kumar served the party and the nation with unparalleled zeal and dedication.
Defence Minister Nirmala Sitharaman also expressed deep sorrow over Kumar’s death.
“Deep sense of grief on hearing that Shri @AnanthKumar_BJP is no more with us. Served @BJP4India @BJP4Karnataka all along. Bengaluru was in his head and heart, always. May God give his family the strength to bear with this loss,” she tweeted.
Union Home Minister Rajnath Singh said he was shocked to learn about the demise of his “senior colleague and friend”.
“Absolutely shocked and pained by the demise of very senior colleague and a friend Shri Anant Kumar ji. He was a seasoned parliamentarian who served the nation in several capacities. His passion and devotion for the welfare of people was commendable. My condolences to his family,” he tweeted.
Union Minister Prakash Javadekar said passing away of Kumar was an irreparable loss for the country.
“It is unbelievable that he is no more. His sudden death has taken away from us a true soldier of the country. My tributes to the departed soul,” he tweeted.
Karnataka Chief Minister H D Kumaraswamy also expressed grief over the death of Kumar, and described him as a “value based” politician, who made significant contribution to the country as an MP and Union minister.
“Kumar’s pro people attitude and activities made him apple of the eye of Bengalurians,” Kumaraswamy said in a condolence message.