The body of the Indian man is expected to reach Raxaul later today.
The protesters threw stones at the police as they rushed back to the bridge where they have staged a sit-in for 40 days.
This morning, the police opened the Birgunj-Raxaul border point after removing the protesters.
About 200 Indian trucks stranded on the Nepal side of the border crossed over into India after the bridge was opened.
Thousands of trucks on the Indian side remain stranded. This includes Nepal Oil Corporation trucks that carry fuel to Kathmandu and other places from the Indian Oil Depot at Raxaul in Bihar.
At around 3 am, about 100 policemen raided the bridge, used batons on the protesters and burnt their tents. About a dozen protesters were injured.
"You will see. These actions will not deter us," said Vijay Kant Karna, a former diplomat, alleging that the new Constitution "doesn't grant people living in plain areas equal rights".
Reports from Nepal's Birgunj town, about eight kilometres from the Indian border, suggest violence and blockades by Madhesi groups in the city.
The Madhesis - natives of the Terai region who share ethnic ties with India - are angry about plans to divide the Himalayan nation into seven federal provinces under the Constitution adopted in September.
There is no word so far on whether trucks from India will be able to cross into Nepal.
Nepal recently signed a deal with China to import petroleum products, after weeks of blaming India for the blockade on the borders.
However, India says it has nothing to do with blockade and it is up to Nepal to find a solution, adding the Indian truckers are concerned about their safety in Nepal.
In the last few months, Nepal is almost totally dependent on India for overland supplies following earthquakes in April this year that killed nearly 9,000 people and blocked crossings from China.
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