Two Indian fishermen were killed on the island in 2006 when their boat broke loose and drifted onto the shore - but no action was reportedly taken in that case.
Regardless of the tribe's protection, Deepak Yadav, a police official in the island chain in the Bay of Bengal, said officers have launched an investigation.
The Sentinelese are said to be at risk of death if they have contact with outsiders as they have no immunity to common diseases like flu and measles.
The American was identified as 27-year-old John Allen Chau.
A tourist has been shot dead with a bow and arrow by tribal people living on a remote protected island in the Indian Ocean.
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The U.S. Consulate in Chennai, in the capital of Tamil Nadu state, said it was aware of reports of the American but declined to comment.
The 27-year-old American came to India on a tourist visa but came to the Andaman and Nicobar islands in October with the express objective of proselytizing, Dependra Pathak, Director General of Police of the Andaman and Nicobar islands, told CNN.
The Sentinelese people who live in the small forested island are known to resist all contact with outsiders, often attacking anyone who comes near.
Director Stephen Corry said the Indian government had recently eased restrictions on foreign tourists, allowing them to visit a host of inhabited and uninhabited islands-although not including North Sentinel. Taking photos or otherwise recording them can be punishable with up to three years in an Indian prison.
Seven local fishermen have been arrested for allegedly facilitating the man's trip, police said.
This member of the Sentinelese tribe was photographed firing arrows at a helicopter which was sent to check up on the tribe in the wake of the 2004 tsunami. In 2017, the government clarified that the Sentinelese are identified as an "aboriginal tribe" and that videos showing them can not be uploaded on social media or the internet.
The 2011 survey only spotted 15 Sentinelese on their island - the count was done from a distance due to the danger in approaching the tribe.