Fire crews from Dudley, Tipton and Brierley Hill spent more than two hours tackling the blaze in Bagnall Street, which started at around 4pm.
The flames also damaged a fence and summer house belonging to a house adjacent to the yard.
Police are not treating the fire as suspicious.
James Round, spokesman for West Midlands Fire Service, said firefighters had remained on site to dampen the smouldering wreckage.
Lee Page, spokesman for West Midlands Police, said: "Officers attended the scene and found nothing to suggest arson was involved."
West Midlands Fire Service are currently operating with a skeleton staff due to a 24-hour strike which started at 9am this morning.
As a result of the dispute there are just 26 fire engines deployed in the whole of the West Midlands.