The Delhi women's minister has been sacked after a 'sex video' showing him kissing two women was leaked to the media, in the latest scandal involving the Indian capital's government.

Women's and children's minister Sandeep Kumar was removed from his post by the Delhi chief minister late Wednesday shortly after the "objectionable" tape was sent to him and national television stations.

"We never try to cover up wrongdoings when evidence comes up against our ministers or party workers, unlike other parties," chief minister Arvind Kejriwal said on Thursday.

"Recd (received) objectionable CD of minister Sandeep Kr. AAP stands for propriety in public life," Kejriwal said on Twitter late Wednesday, announcing the sacking and referring to his anti-corruption Aam Aadmi Party.

Kumar, a married father of one, said he was the victim of a political conspiracy over the tape ostensibly showing him on a bed dressed only in his shorts kissing one of the women.

Only snippets of the video have been aired on news channels but they, along with photographs, appear to also show him kissing another woman.

"This is a conspiracy against me because I was becoming a prominent face of the Dalit community in the city," Kumar told reporters on Thursday, referring to India's lowest social Dalit caste.

"Check the authenticity of the CD. It is a matter of investigation, a conspiracy to suppress me."

The opposition Bharatiya Janata Party (BJP), which rules at the national level and has been embroiled in bitter disputes with Kejriwal's government, called on the chief minister to resign.

Kejriwal, an anti-corruption campaigner turned politician, oversaw a dramatic landslide victory over Prime Minister Narendra Modi's BJP at city elections last year.

But his government has been hit by controversy, with the law minister arrested in June last year on allegations his law degree was fake and another minister removed over corruption allegations.