Gopinath Munde, 64, was on his way to the airport for a victory rally in his home state of Maharashtra, when his sedan was hit by a car. He died in hospital.
"My tributes to a dynamic leader whose premature demise leaves a void hard to fill," Modi said in a tweet, amid a flurry of tributes from allies and political opponents. "Condolences to Munde's family. We stand by them in this hour of grief."
Dozens of BJP supporters swarmed the party headquarters where Munde's body was brought in a flower-bedecked truck. Modi laid a wreath and consoled members of Munde's family, including his daughter.
Modi had entrusted to Munde the crucial task of spearheading a battle on poverty in the countryside, home to more than half of India's population of 1.2 billion, but which contributes just 14 percent of gross domestic product in Asia's third-largest economy.
The minister was sitting in the back of his Maruti SX4 sedan when it was hit on the side by a Tata Indica saloon, whose driver police said was in custody. Munde's driver and a personal assistant survived.
Doctors tried to revive Munde for 50 minutes after he was taken to the All India Institute of Medical Sciences, a hospital spokesman said. "There was no spontaneous breathing, no pulse, no cardiac activity," he added.
The OBC face of BJP in Maharashtra and former Deputy CM, Munde was all set to spearhead the party's campaign in the upcoming Assembly polls in the state to wrest power from the Congress-NCP combine.
The 64-year-old had always harboured the ambition of becoming first BJP CM of Maharashtra. A known detractor of NCP chief Sharad Pawar, Munde was credited with neutralising the Maratha politician's influence to such an extent that the Sena-BJP combine came to power in the 1995 Assembly polls and he became the Deputy cm.
Brother-in-law of slain BJP leader Pramod Mahajan, Munde hails from a poor family in the backward Marathwada region and was brought into politics by the late BJP leader Vasantrao Bhagwat, who also groomed several others including Pramod Mahajan.
Modi along with the BJP leadership had handpicked Munde to lead the party's campaign in the state where assembly polls are due in four months.
Munde, who was the deputy Leader of Opposition in 15th Lok Sabha, won the Lok Sabha polls this time despite Pawar making the Beed seat a prestige issue.
He also served as general secretary of the party at the national level and as chairman of the Committee on Chemicals and Fertilisers in the outgoing Lok Sabha.
Born on December 12, 1949, and hailing from Nathra village in Beed district, Munde was member of Maharashtra Legislative Assembly for five terms, 1980-1985, 1990-2009.
He was born to Pandurang Munde and Limbabai Munde in a middle class Vanjari (caste) farmer's family.
He is survived by wife and three daughters - Pankaja, Pritam and Yashashri.