The suspect's name and other details of the arrest were not provided, the Idaho Statesman reported. A news conference was scheduled for 7 p.m. local time.
A Zoo Boise security guard spotted two men running from the area where the monkey was found fatally injured early Saturday, but investigators had yet to determine what prompted the attack on the primate.
"It's maddening ... a lot of people are angry over this," Boise police spokeswoman Lynn Hightower told the newspaper Monday.
A necropsy found the animal died of blunt force trauma to its head and neck.
Couple calls 9-1-1 over missing hash browns; assault McDonanld's employees
Workers accuse National Zoo of animal mismanagement