Strict conditions apply to the permit, which came into effect in late August, and the treatment has to be conducted under the supervision of a doctor.
Despite the widespread evidence that cannabis can help MS patients, as well as cancer and HIV/AIDS sufferers, counter their pain and assist in curbing weight-loss, German doctors are not allowed to prescribe it.
A synthetic alternative is available in the form of Dronabinol, the active ingredient in cannabis, but the state health insurance will not pay the costs, and 60 capsules can cost up to $2,000.
Many patients resort to illegal sources for the drug, enduring the hassle of negotiating the drug-dealers' milieu and running the risk of brushes with the law.
Police and the courts in Germany tend to take a relaxed view on the possession of small quantities of cannabis, but practice varies from state to state.
Claudia H was one of those prepared to run the risks, even though at the age of 51, this ran counter to her nature.
"I tried out all the legal medications, but the side effects were unacceptable," the software technician told the Sueddeutsche newspaper.
She has been unable to walk for the past 10 years, and her condition began to deteriorate markedly five years ago.
"I couldn't sleep at night as a result of cramps, but if I took tablets, things were worse the next day," she said. Dronabinol did not help either.
Then Claudia H saw an article in a magazine for MS patients. "I wanted to try it, and my doctor was in support," she said. "I got hold of some cannabis, and now I make tea two or three times a week when the symptoms are bad."
She was immediately convinced. The paralysis was reduced, with the effects continuing into the next day.
Claudia H says she experiences no sensation of intoxication and no indication she has become dependent on the drug, but her medication remained technically illegal.
Now a central regulatory body called the Federal Opiate Authority has given Claudia H special permission to continue. Previous requests had been automatically turned down.
Other MS patients still have to apply individually for that permission, but the hope is that there has at last been a change in official thinking.