Renu Dahal, 39, daughter of UCPN-Maoist chief Prachanda, was arrested for her alleged involvement in vandalising vehicles for defying the strike, the police said.
Major markets were closed, educational institutions were shut down and vehicular movement came to a halt during the strike in Kathmandu and other major cities.
Opposition protesters clashed with police at Bijulibazaar of Kathmandu this morning when the agitators tried to vandalise a police van. The police had to fire five rounds of tear gas shells to bring the situation under control.
The agitators also burnt a taxi in Koteshwor area of Kathmandu on the first day of the three-day strike.
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In Pokhara, the tourist hub of western Nepal, the agitators vandalized four vehicles. Police arrested four protesters for their involvement in vandalism.
A passenger bus was set ablaze in Jaleshwor Municipality in southern Nepal for defying the strike.
The strike was backed by the UCPN-Maoist, Madhesi Front and some fringe ethnic-based parties.
They have opposed the government's move to promulgate the Constitution through voting process, demanding consensus on the key issues such as federalism and forms of governance.