On Tuesday, a crude bomb went off after voters lined up to cast their ballots at a busy polling station in the heart of Katmandu, seriously wounding the boy, police official Hemant Pal said.
"This 8-year-old boy was playing with his friends in the neighborhood when he picked up the bomb, assuming it was something to play with," Pal said.
The boy's uncle, Uttam Shahi, told The Associated Press that the child was knocked unconscious and would likely lose several fingers.
Two women suffered minor injuries in the blast.
In Chamundu village, about 400 kilometers (250 miles) west of Katmandu, opposition activists stormed into a polling station and ripped up ballots, said Homnath Thapaliya, the chief government administrator in the area. He said police fired in the air and about a dozen voters suffered bruises as they tried to flee the scene.
The Election Commission said voting was halted in one village in the northeast and there were brief disruptions in four other places.
Candidates from more than 100 political parties competed in Tuesday's vote. The assembly will double as the parliament and choose a government.
But analysts say none of the political parties is likely to get a majority, which could keep the country in a state of political paralysis.
"We can only hope that the politicians will come to their senses and put the country's interest before their own," said Ranju Singh, a university student who voted Tuesday.
The last Constituent Assembly was elected in 2008, following the end of a 10-year Maoist insurgency and the overthrow of the monarchy. But the assembly was riven by infighting and never finished its work.
The result is a power vacuum that has left Nepal without a proper constitution for nearly seven years.
Some of the political disagreements center on whether to divide the country into a federal system based on ethnic groups or strictly by geography. But the parties mostly squabble over who gets to lead the nation.
The United Communist Party of Nepal (Maoist), the party of the former communist rebels, is hoping to repeat the last election and emerge as the largest party. Its main competitors are the Nepali Congress and Communist Party of Nepal (United Marxist Leninist).
Nepal has 12 million registered voters.
Election official Upreti said vote counting would begin late Tuesday in some urban areas. First results would begin coming in Wednesday, he said.
"We expect the final results to take at a least week and a maximum of 10 days," Upreti said.
Ballot boxes have to be collected from remote mountain villages, which will take time.