The emergency services were called to the two-vehicle collision at around 1am today (January 21).
Firefighters freed a man and a woman who had become trapped in a vehicle, while a third person managed to free themselves.
Paramedics treated all three patients at the scene and took them to hospital.
Their injuries are understood from the Met Police not to be life-changing.
The A13 was closed for hours following the crash but has since reopened and traffic has returned to normal.
A London Fire Brigade spokesperson said: “We were called at 0106 hrs today to a report of a road traffic collision on the A13 in Rainham.
“Two vehicles were involved.
“Firefighters released a man and a woman from each of the vehicles, who were both confirmed to be trapped.
“They were both taken to hospital by London Ambulance Service along with a third patient, who was able to leave a vehicle before firefighters arrived.
“Two fire engines from Wennington and Barking fire stations and a fire rescue unit from East Ham Fire Station attended the scene.”
A London Ambulance Service spokesperson said: “We were called at 1.02am today (21 January) to reports of a road traffic collision on the A13, Rainham.
“We sent resources to the scene including ambulance crews, paramedics in fast response cars and an incident response officer.
“We treated three patients and took them all to hospital.”
