Rita Bahuguna Joshi, the chief of the Congress party in northern Uttar Pradesh state, was placed under 14 days custody pending investigations for allegedly promoting social enmity, insulting a woman's modesty and insulting a person of lower caste.
No charges have been filed yet, but the three offenses are punishable by up to 10 years in jail.
Joshi's house in Uttar Pradesh's capital Lucknow was set on fire on Wednesday night, hours after she made a speech criticizing state Chief Minister Mayawati, who uses only one name.
Joshi said her comments were taken out of context.
Her speech was about the law and order situation in Uttar Pradesh and the increasing number of rapes in the state. She cited a few cases in which some women were paid 25,000 rupees ($520) compensation after being raped.
Joshi said simply compensating the women with money was not enough. Women who are raped should "throw the money at Mayawati's face and tell her 'you should also be raped and I will give you 10 million rupees ($210,000),"' she said in the speech, broadcast by several television networks.
Such crass comments are commonplace in Indian politics, and Mayawati used almost exactly the same words while referring to a political rival's daughter and nieces a few years ago.
On Thursday, Joshi said she was only trying to "expose a chief minister who has no sympathy for women."
"I regret what I said in a fit of anger. If it is being misconstrued, if it's being misinterpreted, it is being taken out of context, then I regret it," she said.
"I am myself a woman and I should not have spoken these words ... I really apologize," she said.
Mayawati appealed to her supporters to maintain peace, saying Joshi's "extremely objectionable and vulgar language" should not be used as a pretext for violence.
She said the torching of Joshi's house was "unfortunate" but denied her party cadres were involved.
Mayawati belongs to the Bahujan Samaj Party, which draws its support from low-caste Hindus who for centuries have remained underprivileged in India's deeply hierarchal society.
In recent years, members of low castes have achieved enormous political clout, which became evident when Mayawati took control of Uttar Pradesh, India's most populous state, in May 2007.
The Bahujan Samaj Party is a bitter rival of the Congress, which runs the federal government and some of India's 29 states.
Police have not arrested any of the people who set fire to Joshi's house and four cars parked on the premises.
Suresh Kumar, a gardener at Joshi's house, said eight to nine masked men, armed with bamboo sticks, poured kerosene and gasoline inside the house and set it alight.
The Congress party rallied around Joshi, but said her comments were "uncalled for."
Congress leader Digvijay Singh accused Mayawati's supporters of setting ablaze Joshi's house on her directions.