Vijayan said this after presiding over a cabinet meeting when the media pointed out that those fighting to preserve the traditions of the temple were screening all vehicles on Tuesday to see if they had women in the age group of 10-50.
Two women journalists were prevented from proceeding to the temple town where their OB van was stationed.
The protesters are staying put at Nilakal, about 20 km from the foothills of the temple, located at Pampa.
"Yes, I have also been told that some people have started screening vehicles. Such a thing cannot be accepted. No one can take law into their hands. The government will ensure that nothing of that sort happens. Those who want to pray cannot be stopped," said Vijayan.
He pointed out that the government had made it very clear that it will not file a review petition against the Supreme Court's September 28 verdict allowing women in the age group of 10 to 50 to pray at the famed Sabarimala temple.
"We have already made this very clear that we will abide by whatever the apex court verdict is. Now that the verdict has come, we will implement it," the Chief Minister said.
On Tuesday morning, hundreds of devotees, including a large number of women, protesting against the Supreme Court ruling, gathered at Nilakal and started checking all vehicles bound to the temple town.
The temple opens on Wednesday at 5 p.m. for the customary monthly pujas.
"We are determined that come what may we will not allow a single lady in the age group 10 to 50 to reach anywhere near the temple. It's a matter of life and death and under no circumstances will we allow a breach of tradition," said a middle aged woman at Nilakal.
The protesters are said to be mainly locals and others who have arrived from nearby areas.
Meanwhile, the Travancore Devasom Board (TDB), the custodian of the temple, on Tuesday met the Pandalam royal family, representatives of the Sabarimala Tantri family and other Hindu organisations to see how best the controversy can be resolved.