The facility planned for Black Rock Quarry would be used by Avon and Somerset Constabulary, Gloucestershire Constabulary and Wiltshire Police.
A passing police officer travelling on nearby Valley Road raised the alarm earlier on Tuesday.
No firearms were in the building, which is still being constructed.
Smoke from the fire can be seen from about 20km (12 miles) away.
Chief Constable Nick Gargan tweeted that he had visited the site, close to the force's headquarters in Portishead, to see the damage for himself.
He described it as “heart-breaking”.
“Thankfully there don't appear to be any casualties, but the fire is still burning so it's impossible to get into the building,” he said.
An Avon Fire and Rescue Service spokeswoman said six fire engines and a turntable ladder were on site to tackle the blaze in a 200m (650ft) by 50m (160ft) building.
“When crews arrived just after 4.30am the building was well alight with fire affecting about 50% of the building,” she said.
“At this stage there is no indication of the cause and firefighters are expected to be at the scene for much of Tuesday.”
The site, which will contain two indoor firing ranges and classrooms, is planned to open next year.
Valley Road remains closed and motorists are being advised to take alternative routes.