Ali Zamani, Governor of Bavanat County, said the incident took place late on Friday in Dareh Bagh protected area, adding that a hunt is underway to find the fugitives.
The victims were identified as Mohammad Farahmand and Reza Bahrampour. The injured ranger was taken to hospital for treatment.
Iranian lawmakers passed laws in July 2019 and June 2020 to allow rangers to carry and use firearms in conflicts with poachers.
Iran has over 3,500 forest rangers and over 150 of them have been killed while protecting the environment since 1979