Bryson has written to President Barack Obama that he is taking a medical leave "so that I can focus on resolving the health issues that arose over the weekend", a statement released by the department said.
The 68-year-old Commerce Secretary struck a car twice on Saturday afternoon near a traffic light and then rammed into another vehicle with his car.
Police found him unconscious in his vehicle and government officials said that he had suffered a seizure. The authorities have so far not charged him with a felony hit-and-run.
Bryson was driving a Lexus in San Gabriel, North East of Los Angeles when his car struck the rear of a vehicle that had stopped for a passing train.
