George Obama was arrested on charges of possession of marijuana and resisting arrest, CNN reported.
Inspector Augustine Mutembei, the officer in charge, said Obama, who is in his mid-20s, is scheduled to appear in court Monday.
Obama told CNN in an interview from the Nairobi jail where he is being held that he denies the charges.
"They took me from my home," CNN quoted him as saying. "I don't know why they are charging me."
George Obama and the president barely know each other, the network reported, noting that George Obama was one of the president's few close relatives who did not go to the inauguration in Washington last week.
In his memoir, "Dreams from My Father," Barack Obama describes meeting George as a "painful affair."
Obama's Kenyan father died in an auto accident when George was just six months old.