State officials said Brown, 74, will continue to work while he receives radiation treatment, The Sacramento Bee reported Thursday.
"Fortunately, this is early-stage, localized prostate cancer, which is being treated with a short course of conventional radiotherapy," his doctor, oncologist Eric Small, said in a statement. "The prognosis is excellent, and there are not expected to be any significant side effects."
Brown's office said treatment should be completed in early January.
Officials declined to discuss the matter beyond the doctor's statement, including when Brown was diagnosed or began treatment, the Bee said.
In April 2011, Brown underwent a procedure to remove skin cancer from his nose.
Notable deaths of 2014 [PHOTOS]