The separate incidents occurred in the Pobitora Wildlife Sanctuary in the northeastern state of Assam, the Press Trust of India reported.
A woodcutter died after an adult rhino gored him, forest officials said.
In the other incident, five people, including a woman, on a sandbar of the Brahmaputra River were hurt when a tiger crossing into the sanctuary from Orang National Park attacked them.
The injured were taken to a hospital in Morigaon.
Park officials are hunting for the tiger.