All but one of the dead from the fire which began on Monday at the centre in the south-western town of Titisee-Neustadt, were handicapped, police said. The other person who died was a 50-year-old woman carer. Nine people were badly hurt and a further five suffered more minor injuries, officials said.
Initial indications suggested the fire was sparked by an explosion after gas escaped from a heater for unknown reasons and ignited, a spokesman for the Freiburg public prosecutor's office told a news conference.
“The investigations are in this respect not finished," Peter Häberle said.
A preliminary investigation against unknown persons into suspected negligent manslaughter and negligent arson had been opened but did not mean prosecutors already had suspicions in this direction, he said.
"Everything's pointing to an accident," he added.
President of Freiburg's government Bärbel Schäfer said fire protection precautions at the workshop had been "absolutely correct" and the rescue operation had been "exemplary".
Hundreds of fire fighters backed by helicopters had battled the fire at the workshop run by the Roman Catholic Caritas welfare association, for the mentally and physically disabled which made Christmas decorations among other things.
Candles have been placed outside the modern building whose windows were broken, and police stood at the entrance while more officers combed through the blackened interior.
Up to 60 people were in the centre at the time of the fire, which broke out just before 2 pm and spread quickly, damaging one floor of the site in Titisee-Neustadt, about 35 kilometres from the city of Freiburg.
Pope Benedict XVI sent his condolences, saying in a telegram he would remember in his prayers the victims of this "tragic accident", according to the Freiburg archbishopric.
A memorial service has been planned for Saturday at a local cathedral, the mayor's office said.
Among the dead were 13 disabled people, of whom 10 were women aged between 28 and 68, according to a police statement.
Gotthard Benitz, of the Titisee-Neustadt fire service, said earlier that the fire began on the ground floor of the building which also had a basement and an upper floor.
"The victims were all on the same floor where the fire was," he said adding this was the only area to have sustained fire damage and the stairwell had remained smoke-free meaning those on the other two floors had been able to use it.
He also said fire fighters had been prepared for dealing with an emergency at the workshop as practice fire alarms were regularly carried out there, with the last one having been last year.
The head of Caritas in Germany, Peter Neher, told ZDF public television that emergency practice drills were carried out regularly.
“But everyone knows who has taken part in such a drill, that the practice is one thing and when it's really an emergency situation, everyone reacts very individually," he said.
Local resident Dietlinde Kerler said she had thought a practice drill was underway initially as she watched from her balcony.
"Those in wheelchairs came out of the back and they even carried one... Only then did we notice that it was smouldering, that it was burning, the real thing," she said.