The blaze happened at an address in Potters Lane on Wednesday night.
West Midlands Fire Service was called to the scene at 11.52pm and sent 10 firefighters from Wednesbury and West Bromwich fire stations.
It is believed the blaze was caused by another which was left unattended in a large metal container.
The first crews arrived in under two minutes and firefighters used a hose reel jet to extinguish the flames.
A spokesman for West Midlands Fire Service said: "There was a fire involving rubbish behind the property in Potters Lane.
"The crews used hose reel jets to extinguish it.
"It was quite tricky in terms of the environment. There was poor lighting and gas cylinders nearby.
"Just after 12.30am crews were damping down.
"They had to force their way into the building that the fire was near to, just to check the fire hadn't gotten in - and fortunately it hadn't."
He added: "It involved approximately three tonnes of general waste on fire.
"It is believed to have started by a fire which had been left unattended in a large metal brazier.
"There was superficial damage to the rear of the factory unit.
"They also moved the gas cylinders to a place of safety."
The alarm was raised by Wednesbury South councillor Ian Chambers, who praised firefighters for their rapid response.