Ms Lankesh, who was "known for her strident anti-establishment views and writings against Hindu fundamentalists, was never afraid of speaking truth to power," the rights body said.
"Her assassination must be thoroughly investigated and the perpetrators brought to justice. The police must investigate whether she was killed because of her journalism," Asmita Basu, Programmes Director at Amnesty International India, said.
Gauri Lankesh, 55, was the editor of Gauri Lankesh Patrike, a Kannada weekly. She was widely regarded as an independent and outspoken journalist and activist, and a fierce critic of hardline Hindu groups in Karnataka.
"Critical journalists and activists have increasingly faced threats and attacks across India in recent years. State governments must act to protect those whose voices of dissent are being silenced," Ms Basu said.
The Committee to Protect Journalists has said that there have been no conviction in any of 27 cases of journalists "murdered for their work" in India since 1992, the statement said.