West Midlands Fire Service said more than 15 fire engines were at the Smurfit Kappa plant, a mill that packaging papers, in Nechells.
About 100 firefighters remain at the scene of the blaze in Mount Street, which broke out shortly after 22:00pm on Wednesday, according to media reports.
The fire service said no-one has been injured and the fire was now contained to the seven-acre yard of the site.
People living near the plant, close to the M6 motorway, were urged to stay indoors with windows and doors shut, the material burning is only thought to be cardboard and non-toxic.
A West Midlands Fire Service spokesman tweeted: “Fire at Smurfit Kappa is in a very large outdoor storage area. Approx 10,000 tons of recycled cardboard bales are ablaze.
“Fire is contained to storage area, high winds are hampering fire fighting, however crews and other agencies are working extremely hard to bring blaze under control.”
