At its height about 100 firefighters were battling the fire, at a branch of building supplies firm Jewson in Moor Road, Hunslet, in the early hours of this morning.
Steve Holmes, of nearby Prospect Crescent, who filmed the explosion, said the fire seemed to have started on one side of an outdoor yard being used to store materials.
He said: "There were a few explosions then, whoosh, in around five or 10 minutes it had gone round the corner."
Mr Holmes said at first the firefighters had been struggling to get to the fire in the yard, which is surrounded by spiked metal fencing.
He said they began by climbing over the fence with ladders.
He said: "They then got fed up with going over the fence and cut a unit out of the fence."