An Indian national was killed Monday when Nepal police fired into a crowd of protesters who were trying to block a border checkpoint, a spokesman said.
"Police warned the protesters to disperse but they did not listen, compelling security forces to open fire," said Nepal police spokesman Kamal Singh Bam.
"An Indian national was wounded and died after being taken to hospital."
Four police suffered injuries in clashes with demonstrators at the checkpoint in the southern town of Birgunj, around 90 kilometres (55 miles) south of Kathmandu, Bam told AFP.
He could not confirm if any other civilians were injured in the violence.
Police earlier used batons to disperse protesters angered by Nepal's new constitution who had blocked the bridge crossing in Birgunj since September 24, cutting off vital supplies and forcing fuel rationing in the landlocked Himalayan nation.
The protesters are from Nepal's Madhesi ethnic minority, who mainly live in the southern plains. They say the internal borders laid out under a federal system in the new constitution will leave them politically marginalised.
More than 40 people have been killed in clashes between police and people protesting against the constitution, which was introduced in September after a deadly earthquake pushed warring political parties to reach agreement.
The fuel crisis has soured ties between Nepal and its powerful neighbour, with authorities in Kathmandu accusing New Delhi of imposing an "unofficial blockade" to show its dissatisfaction with the new constitution.
New Delhi denies the charge and has urged dialogue with the protesting Madhesis, who have close cultural, linguistic and family ties to Indians living across the border.