Police said the case, the first since the missing of the youths came to fore last week, was registered against Yahiya, husband of city-based Merin alias Mariyam, who went missing in the Middle East about a month ago, and one Quraishi from Mumbai, on a complaint by her brother.
They also compelled her to join the IS her brother alleged, police said.
The complainant also alleged that both Yahiya and Quraishi even tried to covert her to Islam and compelled him to join the IS during his stay with his sister in Mumbai, they said.
Merin, who hailed from a Christian family in Kochi had married Yahiya, her former classmate, and converted to Islam while she was in Mumbai.
Most of their families suspect they may have joined the Islamic State.
Chief Minister Pinarayi Vijayan had said the matter was serious and would be examined.
Police said they haven't got any concrete information about alleged terror link of Yahiya and Quraishi and the case under UAPA had been registered against them on the basis of the complaint by Merin's brother.
Senior Congress leader and Thrikkakara MLA P T Thomas had recently alleged that Zakir Naik's Islamic Research Foundation is suspected to have a role in "brainwashing and radicalising" the youths from Kerala who went missing in the Middle East recently.
