Cardinal Baselios Cleemis Thottunkal was speaking before he visited a nun in hospital, who was gang-raped by eight men at her convent and Christian school, leaving her with critical injuries.
Tougher laws against the killing of cows recently came into force in two Indian states, because traditional Hindus view the animal as sacred.
Maharashtra, a western state, banned the sale of beef in February, whilst the northern state of Haryana instated new penalties for cow slaughter.
The cardinal said: "The country has a responsibility towards all of us, every human being, and not just cows."
According to The Hindu newspaper, he also called for the country to become more open to those of all faiths and none.
The Indian Constitution enshrines religious freedom in law, and it also defines India as a secular country, meaning it has no official state religion.
Prime Minister Narendra Modi's Hindu-nationalist government has been accused of not doing enough to protect religious minorities in the country.
Recently, the Secretary General of the World Hindu Council said it was part of Christian culture to "exploit nuns". Previously, the leader of India's biggest Hindu volunteer organisation said Mother Theresa only worked in India to convert people to Christianity.
Protests have occurred after a spate of attacks against churches in the last six months, with large demonstrations happening after the nun's assault.