The policemen were on their way to a local college to provide security when their vehicle hit the mine near Maniram village in Rupandehi district about 200 kilometres southwest of Kathmandu.
Ganga Dutta Aaasthi, chief administrative official in the district, said rain made visibility poor on the road. He said police suspect Maoist rebels planted the explosives on the road.
The injured policemen have been transported by helicopter to nearby hospitals. Reinforcements have been sent to the area and the attackers are being searched for, the official said.