The bomb was apparently meant to target a security forces vehicle but landed on the pavement at Nepalgunj, a border city 500 km west of Katmandu.
The people injured by the attack at 8:30 p.m. local time on Tuesday are being treated at the local hospital, said police official Shyam Khatri.
Doctors at the local hospital said all the wounded people are out of danger.
The rebels, who claim to be inspired by Chinese revolutionary Mao Zedong, have been fighting since 1996 to abolish Nepal's constitutional monarchy and set up a communist state.
The guerrillas have stepped up violence since King Gyanendra took over absolute power in February promising to quell the insurgency, which has left more than 11,500 people dead since 1996.