Ms Sahgal, 88, is the niece of India's first prime minister Jawaharlal Nehru. She received the literary award in 1986.
In a statement explaining her decision, titled "Unmaking of India", she refers to the recent mob killing of a Muslim man over rumours that he had eaten beef, and also the killings of rationalists MM Kalburgi, Narendra Dabholkar and Govind Pansare.
"In memory of the Indians who have been murdered, in support of all Indians who uphold the right to dissent, and of all dissenters who now live in fear and uncertainty, I am returning my Sahitya Akademi Award," says the writer known for her outspoken views. The right to dissent, she asserts, is an integral part of India's Constitution.
Speaking to NDTV, Ms Sahgal questioned Prime Minister Narendra Modi's silence.
"The Prime Minister is absolutely silent. He has uttered no word of condemnation at all at these incidents. The whole country wishes the Prime Minister to make a statement because the situation is getting more and more serious," Ms Sahgal said.
"Under Modi we are going backwards, regressing, narrowing down to Hindutva...there is rising intolerance and lots of Indians are living in fear," she commented.
In her statement, she also accuses the Sahitya Akademi, the organization that promotes Indian literature, of silence.
Ms Sahgal was known for her strong stand against the Emergency of 1975-77 imposed by Indira Gandhi, during which several opposition leaders were jailed.
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