The 54-year-old and his son were returning from a day’s hunting on Wednesday when the accident happened.
As they were walking down a mountain path at 2,200m, the father’s gun went off, shooting the son in his right leg.
Swiss air ambulance service Rega transported the man to hospital.
Uri cantonal police have opened an investigation into the incident.
Accidents during hunting season are not uncommon in Switzerland.
Last autumn a 57-year-old from Ticino was killed when he slipped down a steep slope whilst out hunting, accidentally shooting himself in the process.
In 2012 a 60-year-old was shot by hunters in the canton of Fribourg after they mistook him for a wild boar. He was in fact picking cannabis leaves.
According to Swiss hunting organization JagdSchweiz there are 30,000 active hunters in Switzerland.