Protests are ongoing after India's top court last month ended a ban on the entry of women of menstruating age into the Sabarimala Temple.
Suspected Hindu radicals attacked a spiritual retreat founded by a preacher who backed letting women enter a renowned Indian temple, police said.
The incident heightened tensions in southern India where police have rounded up more than 2,000 people suspected of taking part in protests to stop women from worshipping at the Sabrimala shrine.
Attackers set ablaze two cars and a scooter outside the ashram in the early morning attack in the southern city of Thiruvananthapuram, police said.
They also placed a wreath outside the retreat condemning Swami Sandeepananda Giri, its founder, who had backed a Supreme Court order ending a longstanding ban on women of childbearing age entering the temple complex.
"We are investigating the matter. No arrests have been made so far," a Thiruvananthapuram police spokesman said.
Kerala state Chief Minister Pinarayi Vijayan condemned the attack on the ashram.
He said in social media posts that such disputes had to be "dealt with at an ideological level".
"We will not let anyone take law and order into their hands," Vijayan added.
Police have launched a major search operation across Kerala state this week and said more arrests are likely as they sift through video footage of attacks on women devotees and police near the Sabrimala temple.
The ruling Bharatiya Janata Party's president Amit Shah slammed the state government for the arrests and use of "brute force" against its party workers and rightwing allies, who were among the thousands arrested.
Shah told a public gathering in Kerala on Saturday that his party would stand by its arrested followers.
"It's a well-planned conspiracy to destroy the sanctity of temples in Kerala by the communists," he said.
The protests erupted as the temple opened for the first time since the Supreme Court last month ended the ban on women of menstruating age from worshipping there.
The court is to hear new petitions challenging its ruling from November 13, just before the temple is due to open again.
Sabarimala devotees believe letting the women in goes against the wishes of the temple's celibate deity.