The male rider was travelling along Foundry Mill Drive in the Seacroft area of the city when his moped collided with a BMW.
The blue BMW 530 was being driven in the opposite direction, close to the junction with South Parkway.
The moped rider was taken to hospital with serious leg and head injuries.
A spokesperson for West Yorkshire Police said: "He remains there in a stable condition today and his injuries are not believed to be life threatening.
"The BMW driver has been spoken to by officers."
Police enquiries are continuing into the crash which happened shortly before 8pm yesterday. (June 8)
Anyone who witnessed the collision, or saw either vehicle being driven in the area before it occurred, is asked to contact PC 2494 Robson at the Eastern Area Roads Policing Unit on 101, quoting reference 13180278260.