Fire chiefs said the blaze would last into the night as more than 100 firefighters tackled it.
People across the city saw thick, black plumes of smoke rising from the site.
Ambulance crews also rushed to the scene at Tyseley Industrial Estate, but there are no reports yet of any casualties.
The West Midlands Fire Service, which said it had received high numbers of calls, sent 10 appliances plus specialist appliances.
Police warned of harmful fumes, and fire chiefs advised residents to keep doors and windows closed, despite the heatwave.
A machine operator working nearby said he and colleagues heard “several bangs”.
“We only noticed the fire when we were clocking out of work. We were already leaving the building before the fire engines arrived,” he told Birmingham Live.
“It was quite scary but we just had to make sure we were out of the area as soon as we could be.”
The smoke caused severe congestion on roads in the area, with buses badly delayed. It could be seen from as far as Birmingham Airport, the city centre, Solihull and Edgbaston.
The ambulance service’s hazardous response team also went to the scene.
The cause of the fire is not yet clear.
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