Some 80 firefighters tackled the blaze at Ney Ltd, Siskin Drive, which was reported at 17:05 BST on Wednesday.
West Midlands Fire Service said it brought the fire under control shortly before midnight.
A service spokesman added that the building had "partially collapsed". There are are no reports of injuries.
A 400m exclusion zone, set up as a precautionary measure because of acetylene cylinders inside the factory, has been lifted and the airport has re-opened after being closed overnight.
Emergency services hope to partially open Siskin Drive to allow traffic in and out of Middlemarch Business Park later.
West Midlands Fire Service's assistant chief fire officer, Phil Hales, said crews from West Midlands and Warwickshire had been dealing with the fire that created a smoke plume "seen from many miles away".
Mr Hales said: "At the height of the fire we had over 15 fire engines and special appliances in attendance with up to 80 firefighters and officers working.
"The building has collapsed inwards. The bits that haven't collapsed have been very severely damaged.
"There will be an assessment of the building and we will work very closely with the building owners to see what salvage or demolition arrangements can be put in place.
"It's made it very difficult for us to access it.
"There's a lot of water run-off from the fire and we've got a river close by so we have to work with the Environment Agency to make sure we don't pollute things.
"We're working close with the police because we want to get the roads back open and get businesses back to normal as quickly as possible."