Police say he looked intoxicated, but Congressman Patrick Kennedy says it was sleep and anti-nausea medication that made him drowsy.
Kennedy crashed his car near the Capitol early Thursday.
He issued a statement saying the attending physician for Congress had prescribed a medication to treat Kennedy's inflammation of the stomach and intestines.
The statement also said he apparently became "disoriented from the medication" and drove the few blocks to the Capitol Complex believing he needed to vote.
No sobriety tests were conducted at the scene. An officer said Kennedy appeared to be staggering when he left his vehicle.
Kennedy, who says he didn't ask for any special consideration, was driven home by Capitol police.