Brown, 78, will not miss any work days while undergoing treatment, his office said, which is expected to occur between late February and early March.
The California governor's oncologist issued a statement saying Brown's prognosis is "excellent."
"Fortunately this is not extensive disease, can be readily treated with a short course of radiotherapy, and there are not expected to be any significant side effects. The prognosis for Governor Brown is excellent."
Brown had treatment for the same form of cancer in 2012.