Customs officers ordered that 28,000 copies of the weekly magazine should have stickers placed over a diagram showing how control of Kashmir is split between India, Pakistan and China.
Both India and Pakistan claim the whole of the Himalayan region and have gone to war twice over its control since 1947.
New Delhi imposes tight restrictions on all maps, insisting they show all of Kashmir as being part of India.
"India is meant to be a democracy that approves of freedom of speech," John Micklethwait, editor-in-chief of The Economist, told AFP. "But they take a much more hostile attitude on this matter than either Pakistan or China."
He added: "This is an act of censorship, and many wise and sensible voices in India see it has no point."
The map appears next to the front-page story of the latest edition of the magazine on "The world's most dangerous border" between India and Pakistan.
The Economist still hoped to distribute the edition once the stickers had been added.
Kashmir is divided between the two nuclear-armed neighbours along a de facto border known as the Line of Control. It closely matches the frontline of fighting at the end of the first India-Pakistan war over Kashmir in 1947.
"The map is impartial, accurate and fair. We show everyone's claims, and it is also realistic as it shows where the unofficial border actually falls," Micklethwait said.
The magazine has clashed in the past with Indian authorities.
In December an entire issue of the Economist was pulped on the censors' orders over a map of the region, and its publishers predicted the May 21 edition was likely to hit trouble.
"As a point of principle we are against changing our articles," said Micklethwait, speaking by telephone from London on Monday. "So we mentioned the problem in a piece pointing out how touchy India is on this."
The magazine also printed a warning saying the map was likely to be censored. "Unlike their government, we think our Indian readers can face political reality," it said.
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