The shooting occurred around 7:30 a.m. (0530 GMT) in a wooded area east of Halden. The three victims belonged to the same hunting party, police incident commander Wilhelm Bjolseth told Norwegian news agency NTB, Xinhua reported.
A male suspect was detained by witnesses and handed over to police when officers arrived. Police said preliminary information indicated that he was not a member of the hunting party and that they did not suspect any other perpetrators.
The injured person was airlifted to a hospital. The motive and the relationship between those involved remained unclear.
Norway's National Criminal Investigation Service, known as Kripos, told NTB that it would assist the investigation following a request from the local police district.
A large emergency response was mobilized, including police officers, ambulances and helicopters.
Halden Mayor Fredrik Holm said local authorities were working to establish a full picture of the situation and arrange support for the relatives of the victims.