Sen spearheaded the revival of Nalanda University in the northern state of Bihar, one of the world's oldest seats of learning, taking over as chancellor in 2012 when it reopened.
But in an open letter to the university's governors, Sen said he has decided not to stay on as chancellor when his current term expires in July because it had become clear that the government did not want him there.
He said India's President Pranab Mukherjee, who has the final say over the appointment, had failed to reply to the board's unanimous recommendation that he remain chancellor.
"This delay, as well as the uncertainty involved, is leading, in effect, to a decisional gap, which is not helpful to Nalanda University's governance and its academic progress," he said.
The government later denied it was trying to "curtail" Sen's tenure.
Sen, who won the Nobel in 1998 for his research into the roots of poverty, came out against India's Hindu nationalist Prime Minister Narendra Modi ahead of last year's election, saying the then opposition leader had not done enough to make minorities feel safe.
He said he was publishing his letter "with a heavy heart" because he was concerned "that academic governance in India remains so deeply vulnerable to the opinions of the ruling government".
Nalanda was a renowned Buddhist centre of learning in its first incarnation, drawing scholars from as far afield as China and modern-day Turkey.
It was known as an architectural masterpiece with temples and parks, but was burnt to the ground by Muslim invaders in the late 12th century.
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