The blaze started yesterday morning while a machine was in use, Avon Fire & Rescue Service said, filling the 20,000sqm building with thick smoke.
Crews from two nearby fire stations were called to the scene on an industrial estate in a mostly residential area on Filwood Road, Fishponds, just after 2am.
An Avon Fire & Rescue spokesman said: “Staff at the site used extinguishers in an attempt to control the fire before the building was safely evacuated.
“Once on scene, firefighters in breathing apparatus entered the large warehouse. The fire had caused the building to fill with thick smoke.
“Breathing apparatus teams used high-pressure hose reels to bring the fire under control. The fire was contained to the printing press and did not spread further within the building.”
Firefighters added the fire is thought to have started accidentally.