In the petition, Vijayan said the Sabarimala temple verdict of September 28 which had allowed entry of women of all ages in the hill-top shrine is "absolutely untenable and irrational, if not perverse".
A five-judge constitution bench headed by then Chief Justice Dipak Misra, had in its 4:1 verdict, said that banning the entry of women into the shrine is gender discrimination and that the practice violates rights of Hindu women.
Until now, girls below 10 years and women over 50 years were allowed to visit the shrine, located in the Western Ghats and about 130 km from Thiruvananthapuram. The temple is hugely popular in southern India.
Meanwhile, Kerala Chief Minister Pinarayi Vijayan has criticised those agitating against his government's move to implement the Supreme Court verdict on the entry of women of all ages into the Sabarimala temple, saying "deliberate" efforts were being made to destroy the state's unity and secular fabric.
"The people of Kerala faced the recent unprecedented floods unitedly but deliberate efforts are now being made to destroy that unity, to destroy the secular fabric," PTI quoted Vijayan as saying.
Last week, the RSS had termed the Kerala government's move to not file a review petition on the Supreme Court's Sabarimala temple order as "unfortunate" and called upon all the stakeholders to come together to address the issue.
"In the case of Sabarimala Devasthanam also, it is an issue of a local temple tradition and faith to which sentiments of millions of devotees, including women, are attached. These sentiments of the devotees cannot be ignored while considering the judgement."
"Unfortunately, the Kerala Government has taken steps to implement the judgement with immediate effect without taking the sentiments of the devotees into consideration," the RSS had said in a statement.
(With inputs from agencies)