The Authority added that those injured had been rushed to the hospital for medical attention and are responding to treatment. The affected exit booth had been closed.
Athi River base commander Agnes Makau told NTV that one motorist died as a result of the accident.
"The Nairobi Expressway is committed to providing a safe and reliable toll road service and would wish to assure the public that they are putting measures in place to avert such unfortunate incidents from occurring," KeNHA noted.
"Motorists are advised to avoid overspeeding and be cautious while on the road."
The first big accident to be reported at the newly launched expressway happened two months ago. The accident involving a personal car occurred after the car hit a fence and landed on the highway.
It's not clear yet how many people were in the car or if there were any casualties. The accident happened just weeks before President Uhuru Kenyatta commissioned the road.
Explainer: Who is a mortician and what exactly do they do?