Members of the Madheshi community say they are discriminated against and are demanding political autonomy and greater representation in parliament.
Policemen injured
The authorities said the police opened fire at the demonstrators after they defied curfew.
They said the protesters also fired at them with home-made guns.
Several policemen are reported to be among the injured.
The demonstrators say they were unarmed and their rally was peaceful.
The protests were organised by a regional group, the Madheshi Janadhikar Forum (Madheshi People's Rights Forum).
On Friday, the Nepalese government announced a three-member team to negotiate with groups that have been staging protests in the southern plains area.
Violent protests began in the region a fortnight ago.
Concerns
The Madheshis say they want more autonomy and more seats in parliament.
They want a federal system for Nepal. But they have rejected federal proposals outlined by the prime minister.
The Madheshis say they will be severely under-represented in the new parliament, and their concerns have still not been adequately addressed.
They say that local people - including many Indians who have crossed over the open border between the two countries - are often denied citizenship certificates and other government documents.
Maoist leader Prachanda has said that while he does not support the violence that has flared in the south, he believes the Madheshis have "genuine demands" which must be addressed.
The southern plain of Nepal, popularly called Terai, is home to the Madheshi people.
They are a mixture of Hindus, Muslims and Buddhists.
Many prefer speaking Hindi to Nepali.
Madheshis make up 33-45% of Nepal's population of 27 million but are vastly under-represented in government and the army, which tend to be dominated by hill dwellers.