Police said the woman, a law student who hailed from a poor family, was subjected to rape and brutal assault using sharp edged weapons before being murdered at her house in Perumbavoor on April 28.
No formal arrest has been made yet in the crime that shocked the state and triggering intense politicking ahead of the May 16 Assembly polls.
Ernakulam Range IG Mahipal Yadav said there were signs of strangulation, smothering and 13 injuries on the woman's neck, chest and at several other places of the body. Some reports said there were around 20 injuries and that the victim's intestines were spilled out.
Police said two persons were initially taken into custody and were being questioned by a police team, headed by Yadav. However, it was not yet known whether they are the real culprits.
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One more person was taken into custody tonight from Kannur in north Kerala and was being brought to Perumbavoor for questioning, police said.
Chief Minister Oommen Chandy described the crime as "shocking" and said the culprits will be brought to book.
No details of the ongoing investigation have been revealed by police. The postmortem report is also being awaited.
According to police, the woman hailing from a poor family was raped and brutally assaulted using sharp edged weapons before being murdered at her house at Perumbavoor in Ernakulam district on April 28. She was found dead in a pool of blood at her one room home at 8 PM on the same day by her mother when she returned from work.
Taking suo motu cognisance of the case on the basis of media reports, state Human Rights Commission Chairman Justice J B Koshy issued a direction to the state DGP in this regard.
"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.
Women's rights activists and political leaders, cutting across party lines expressed their shock at the murder which they believe was a first of its kind in the state for the sheer brutality of the crime.