The disease was detected for the first time in Europe last year in Norway, with three known cases of reindeer infected in a single herd.
In chronic-wasting disease (CWD), a cousin of mad-cow disease and already present in North America, deer brains turn spongy, causing the animal to lose weight and die.
It is contagious among deer and reindeer but not known to pass from animals to humans.
The disease was detected for the first time in Europe last year in Norway, with three known cases of reindeer infected in a single herd and two other cases among moose -- though the latter cases were considered to be of less concern since moose do not live in herds.
To prevent the spread of the disease, the Norwegian Food Safety Authority -- which oversees animal health issues -- called for the slaughter of the affected herd, which has between 2,000 and 2,200 wild reindeer living in the southwestern mountainous region of Nordfjella.
In a letter sent Monday to the authority, the agriculture ministry gave the green light "based on the knowledge we have today and the unanimous recommendations of experts."
The herd, which represents about six percent of Norway's total reindeer population, is to be eradicated by May 1, 2018, the ministry said.
The Food Safety Authority has until June 15 to present an action plan.
Possibilities being considered include rounding up the animals for slaughter, or extending hunting in the region.