The fire broke out at 2 pm and was likely caused by an explosion in a storage room at the workshop in Titisee-Neustadt, in the Black Forest area of Baden-Württemberg, according to the police.
"We can tell you that we have 14 dead. The process of identification is ongoing," said Karl-Heinz Schmid, a spokesman for police in the nearby city of Freiburg. "We also have a large number of injured who have been taken to hospital."
What caused the blast is not yet clear – the centre mainly offers training in wood and metal work or fitting electrics.
Firefighters managed to rescue almost everyone in the building – employees generally had mental or physical disabilities. But 14 could not be saved, and died either from burns or smoke inhalation.
There are around 120 people who work in the Titisee-Neustadt centre, 50 of whom were in the building at the time. Police have asked those who were there when the fire broke out to identify themselves.
Around 300 firefighters from neighbouring regions came to help put out the blaze, which took over two hours to extinguish. Authorities were working to determine the cause of the fire. It was not clear whether chemicals were stored in the building, but the workshop's activities included the treatment of wood.
Pictures showed dense smoke billowing out of the three-storey concrete building and firefighters helping the injured, some in wheelchairs, to helicopters and ambulances.
Alexander Widmaier, head of the local fire department, said the alarm was raised at 1:58 pm local time (1258 GMT) and his firefighters were on the scene within six minutes. He said there was a "massive" amount of smoke that filled the building "extremely quickly."
A source close to Caritas, the welfare association that runs the workshop, said there were 50 or 60 people aged between 20 and 65 in the building when the blaze broke out.
In total, the workshop employed some 120 people with disabilities.
The source, who spoke on condition of anonymity, said the majority were mentally disabled workers who were manufacturing wooden decorations for Christmas as well as other electrical and metal goods.
The building was relatively modern and fully in line with fire regulations, this source stressed. The building was still intact after the blaze was extinguished.
Caritas president Peter Neher said: "We know the colleagues at the scene will do everything to find out the cause for this terrible event."
Chancellor Angela Merkel's spokesman Steffen Seibert tweeted that she was "appalled" by the fire and was receiving updates from Winfried Kretschmann, the state premier of Baden-Württemberg, where the fire took place.
Kretschmann himself said: "My thoughts go out to the victims and my deepest condolences go to their families. The whole of Baden-Wuerttemberg mourns with
Some 25 counsellors were treating relatives of the victims at the scene. The process of identifying the dead was expected to last until the early evening local time. The local Red Cross sent 80 people to lend assistance.
Prosecutors and experts must now investigate the possible causes of the blaze, said a spokesman for the local fire department.
"We are dealing here with people who of course do not react rationally," fire chief Widmaier said.