George Obama, who is in his 20s and barely knows the president, had one joint of marijuana on him, said Joshua Omokulongolo, the police chief in the area.
"He is not a drug peddler," Omokulongolo told The Associated Press. "But it's illegal, it's a banned substance."
George Obama has a court appearance scheduled Monday morning.
He and the president have the same father, who died in a car crash in 1982.
Several of President Obama's Kenyan relatives went to Washington, D.C., for his inauguration, but George was not among them. He lives in Huruma with extended family.
Media reports about him surfaced over the summer, after a magazine article said he lived in a shack and earned a dollar a day. George Obama has called the reports insulting.
"I'm proud of how I live," he told The Associated Press in an interview over the summer. "(The media) are tarnishing the family name."
He also said he was studying to be a mechanic and works with a local youth group in Huruma.
In President Obama's book "Dreams From My Father," he describes George Obama as "a handsome, roundheaded boy with a wary gaze."
George is the youngest of the senior Obama's seven children, born six months before his father died.