Fire crews tackled the incident on Cowper Mount, Harehills, just before 5am today (Monday).
West Yorkshire Police said a Black Volkswagen appeared to have rolled down the sloping street and hit the van.
A police spokesman said: "It is not known how the vehicle rolled or came to be on fire.
"Gas and electricity supplies were isolated for a small number of homes as a precautionary measure.
"There were no known injuries to anyone in the vehicles or to residents."