The figures were taken by the Ministry of Health based on a national registration system, reports newspaper Politiken.
111 different patients were covered by the 131 instances of prescribing, according to the report. As such, some patients were given prescriptions more than once.
53 different doctors have so far made use of the trial scheme to prescribe medicinal cannabis.
"We previously expected around 500 patients to become part of the trial during the first year. A figure of 111 during the first month therefore shows we are well underway," health minister Ellen Trane Nørby said to Politiken.
"A number of doctors are already in dialogue with their patients about the treatment, which the patients will hopefully benefit from. That is positive," the minister added.
Parliament passed before the end of 2017 a law enabling selected patient groups to be prescribed cannabis oil by their general practitioners as part of a four-year trial.
Ailments eligible for the treatment include multiple sclerosis, chronic pain, spinal cord injuries and chemotherapy-induced nausea and vomiting.
But doctors have been reported to be reticent about prescribing the medicine, citing a lack of studies determining its effectiveness and side effects.
The director of the Danish Arthritis Society (Gigtforeningen) said she did not agree with the minister's comments that the trial had made a good start.
"It is very positive that some patients have actually been prescribed medicinal cannabis, but it is still a very small number," Mette Bryde Lind told Ritzau.
The society has been contacted by members whose doctors will not prescribe the medicine, Lind said.
"Over 100 people have been refused because their doctor won't prescribe it. In fact, there is not even a dialogue between the doctor and the patient, so [patients] are also not referred to any alternative," she said.