The attack took place around 2 AM and two cars and a scooter were burnt, they said, adding the attackers also left a wreath at the ashram.
Swami Sandeepananda Giri, who was at the ashram when the incident took place, had welcomed the apex court order permitting women in the 10-50 age group to offer prayers at the Lord Ayyappa temple in Sabarimala.
Condemning the attack, Chief Minister Pinarayi Vijayan, who visited the ashram, told reporters that use of violence reveals the 'ideological abjectness' of the attackers.
"No one will be allowed to take law into their hands. I have visited him and assured that stringent action will taken against the attackers," he said.
"Swami Sandeepananda Giri champions the values of secularism and has been a strong critic against attempts to politicise religious spaces. Our society must rise against such attacks," Vijayan said.
"Differing opinions and dissenting voices should be met ideologically. When they fail to do so, it results in physical assaults. Nobody will be allowed to take law into their hands," he added.
Alleging that RSS was behind the attack, CPI(M) state secretary Kodiyeri Balakrishnan said it showed that the Sangh parivar would go to any lengths to 'silence' secular voices.
Finance Minister Thomas Isaac and Devaswom Minister Kadakampally Surendran visited the ashram.
Flaying the attack on the ashram, Kerala PCC president Mullapally Ramachandran said it took place because the swami had raised his voice against fascist forces and alleged that the Sangh parivar was behind the incident.
Sandeepananda Giri alleged that the responsibility for the attack was on BJP state president P S Sreedharan Pillai, Thazhamon Madom, the family of traditional head priests of Sabarimala temple and Pandalam royal family, also associated with the shrine.
DGP Loknath Behara said strong action would be taken to bring the accused to book.
"We will not tolerate such incidents in the state," he said.
However, BJP district leadership has denied any role in the attack and demanded an "unbiased" probe into the incident.
The saffron party also alleged that the CPI(M) was behind the attack, which was carried out to divert attention from the Sabarimala protests. The state had witnessed massive protests from devotees at various places, including Sabarimala, Nilakkal and Pamba, against permitting women of all ages to enter the shrine, where the deity is 'Naishtika Brahmachari' (perennial celibate), when the temple was opened for monthly poojas from October 17-22.