The man is said to have committed the act on 25 July at their home where he lived alone with his elderly mother.
He threatened to kill her if she told anybody, the Nairobi News reported.
However, the incident came to light two weeks ago at a family gathering when relatives noticed the old woman walking with difficulty and pressed her to explain.
She said her son had instructed her to burn the mattress and the blanket after he raped her, and that it had happened before.
The suspect went on the run, but was arrested on Thursday after residents spotted him.