Junior Environment Minister Dilip Singh Judeo, who has denied the allegations, quit after The Indian Express published the corruption allegations, said Mukhtar Abbas Naqvi, spokesman for the Hindu nationalist Bharatiya Janata Party (BJP) which heads the coalition.
Judeo was a leading campaigner for the BJP in a major round of elections being held in five states. Naqvi blamed the newspaper report on political rivals and said the allegations were false.
The Express said it had a tape of Judeo taking money for favours in mining businesses in his home state of Chattisgarh.
Television channels aired the footage of him taking a wad of cash from a man called Rahul, touching the bills to his forehead and saying: "Money isn't God but swear on God, it's no less than God."
His resignation came soon after a high level meeting at Prime Minister Atal Behari Vajpayee's official residence, called to assess the damage to the image of the government, which came to power in 1998 on an anti-corruption plank.
The allegations could not have come at a worse time for the ruling BJP party, which is preparing to challenge India's main opposition Congress party in assembly polls in four states - Delhi, Rajasthan, Madhya Pradesh and Chattisgarh - on 1 December.
The polls are seen as a litmus test for national elections due by October 2004.
Vajpayee on Sunday said Judeo would have to quit "if found guilty".
"It is a policy of my government to carry out an open probe into all charges of corruption and an inquiry is already being conducted," Vajpayee said.
Shades of Tehelka
The video expose bore an uncanny resemblance to a sting operation by the news website Tehelka, which in March 2001 showed the BJP's then president Bangaru Laxman and defence officials taking bribes.
Laxman was removed as the BJP chief and Defence Minister George Fernandes resigned, although he was reinstated six months later.
In May 2003, junior finance minister Gingee Ramachandran quit following the arrest of his secretary for taking bribes from bureaucrats in return for a promise of a plum posting.