Forest department officials say the turtles may have been hit by trawlers fishing along the Puri beach in Orissa.
Local fishermen often flout the ban on fishing along the coast, disturbing the natural nesting space of turtles, they say.
Olive ridley is one of the five species of marine turtles to mate and nest on India's shores.
The turtles come in "large numbers to Gahirmatha, mouth of rivers Devi and Rushikulya in Orissa coast, for annual nesting", Sarat Chandra Behera, an official of the Puri-Balukhand forest range, told the Indian Express.
"We suspect that they were killed after being hit by fishing trawlers in the sea," he added.
Tens of thousands of olive ridley turtles also come to the shores of southern India to lay eggs every year between January and April.
In 2014, more than 900 olive ridley turtles were found dead along the coast of the southern state of Andhra Pradesh.
More than 150 endangered olive ridley turtles have been found dead along the eastern coast of India.