Police said the two were taken into custody and were being questioned by a police team, headed by Ernakulam Range IG Mahipal Yadav.
However it was not yet known whether they are the real culprits. No details of the ongoing investigation have been revealed by police.
Police said the post-mortem report revealed that the woman, a law student, was subjected to rape and brutal assault using sharp edged weapons before being murdered at her house on April 28.
"Kerala is shocked by the brutal murder of a young woman. The culprits will be brought to book and the severest punishment will be ensured to those who involved into the incident," Chandy said.
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Home Minister Ramesh Chennithala has left for Perumbavoor from his constituency Harippad in Alappuzha to visit the victim's mother.
The brutal murder has shocked the state, with women activists and students taking to the streets, demanding justice for the woman.
"Police have failed to get any lead about the culprits even five days after the incident," CPM state secretary Kodiyeri Balakrishnan had said yesterday.
Rejecting the charge, Chennithala had said a "scientific" probe was on into the incident and asserted that the culprits would be brought to book.
Police have launched a rigorous manhunt to nab the culprits.