Police said they opened fire after protesters threw petrol bombs and stones at security forces, attacked police vehicles and vandalised a local police station in the southern district of Rupandehi.
“Four people were killed when police were forced to fire as the crowd became threatening,” district police chief Rajendra Dhakal told AFP by phone.
“Unfortunately, among them was a four-year-old boy.”
More than 40 people have died in fierce clashes between police and protesters in Nepal’s southern plains that erupted after the main political parties reached a historic deal on a new constitution, under pressure to work together following a devastating earthquake in April.
They include 11 police and the 18-month-old son of a police officer shot dead when protesters opened fire outside his home.
Lawmakers began voting on the charter on Sunday and it is scheduled to be formally brought into being by the president on September 20.
But plans in the bill to divide the Himalayan nation into seven provinces have met with fierce opposition from some minority groups who say the new borders will leave them under-represented in the national parliament.
Nepal began working on a new national constitution in 2008, two years after the end of a decade-long Maoist insurgency that left an estimated 16,000 people dead and brought down the 24 when protesters opened fire outside his home.