The violence comes as the Himalayan country braces for local elections that government opponents have vowed to interrupt.
Several groups of protesters were on Thursday protesting in Pokhara, a resort town 200km west of Katmandu, when police used tear gas and batons to disperse them.
The police later opened fire, injuring a bystander, according to witnesses. The independent Kantipur radio said police arrested dozens of protesters.
Government officials reached by telephone acknowledged that police opened fire on the protesters but refused to say if anyone was injured.
Police arrested 20 politicians and activists who were getting ready to hold a rally in Nepalgunj, about 500km southwest of Katmandu, said Binod Adhikari, the chief administrative officer in the area.
Officials said suspected rebels also abducted a candidate in the neighbouring town of Gulariya. He was taken from his home overnight and has not been heard from since.
Maoist rebels fighting for a socialist state have threatened to take action against anyone who registers as a candidate in next month's municipal elections. Rebels have already been blamed for the assassination of a candidate last week in south Nepal.
Meanwhile, Nepal's one-day registration for municipal elections drew only a trickle of candidates as a general strike by dissidents to protest the polls left the capital nearly deserted.
The country's Maoist rebels and a coalition of the seven top political parties oppose the royalist government's plans for local elections on 8 February, arguing they will legitimize King Gyanendra's seizure of direct control over the central government a year ago.