Furious locals in Budanilkantha in the north of Kathmandu tried to defy the Maoists, who have ordered private and commercial vehicles off the streets and for all shops, offices and businesses to remain closed.
Police said they used tear gas to break up the fighting as Maoist supporters beat up locals frustrated at the shutdown.
Violence also erupted in the town of Birganj, the country's biggest industrial town as a Hindu group staged an anti-strike rally.
Al Jazeera's Subina Shrestha, reporting from Nepal, said a curfew had been enforced in the town following the clashes.
"The Maoists were kept out in a very tight police cordon but they managed to break it," Shrestha said.
"Luckily, torrential rain put an end to the confrontations. But as the strike drags on, perhaps for many more days, there are fears that violence will intensify."
The National Human Rights Commission, an autonomous official body, expressed concern over the increasing problems facing the public as talks between Maoists and the government failed to make progress.
"Medical care has been badly affected. We have had reports of patients being transported back to their homes in wheelchairs," Gauri Pradhan, commission spokesman, said.
"Pregnant women have difficulty getting to hospital. Remote areas are facing acute shortage of essential drugs because transport is affected," she said.
Many hospitals have kept only their emergency wards open as doctors struggle to get to work.
The Maoists have launched their challenge to the government - a loose coalition of 20 parties - ahead of May 28 by when a new national constitution should have been drafted.
But legislators are expected to miss the deadline, leading to a possible political crisis.
"The prime minister needs to step down, and all parties must reach an agreement on how to move forward," Lok Raj Baral, chairman of the Nepal Centre of Contemporary Studies, a pro-democracy think tank, said.
"They must not forget that the constitution still needs to be written and the peace process brought back on track."
Maoist guerrillas fought a bloody insurgency against the state for 10 years before a peace deal was signed in 2006. The left-wing former rebels then won elections in 2008 before falling from power last year.
A second major obstacle facing the country is how to integrate nearly 20,000 former Maoist fighters who are living in UN-monitored camps around the country.
Ordinary Nepalis say they are being hurt by the strike and consumer groups said food was running low and prices had risen.
"I can't go to work and even earn my bread," Ramesh Bhandari, a painter, said.