Nominated member Richard Hay said it looked as if Kerala was losing its earlier glory.
"Does it (Kerala) deserve the description 'God's own country'? It has become a devil's country," Hay lamented while raising the issue.
He and other members raised the issue of Jisha, 27, who was murdered on April 28 in Perumbavoor in Ernakulam. Her body was found badly mutilated.
The brutality has led to comparisons with the 2012 gang-rape in Delhi that shook the nation.
BJP's Meenakshi Lekhi said the young woman's death "was a sad reminder of the Nirbhaya case". She wanted to know why no arrest had been been made.
Days after this incident, another young student was allegedly gang-raped and dumped at Varkala near Thiruvananthapuram, she said.
Admitting that the incident in Kerala was serious, Parliamentary Affairs Minister M. Venkaiah Naidu said "such incidents should not be made into a political issue".
Naidu said he will share the concern of the Lok Sabha members with Home Minister Rajnath Singh and request him to seek a report on the matter.
In the Rajya Sabha, members raised the issue and Social Justice Minister Thawar Chand Gehlot said he will visit Kerala soon.