Authorities said tests showed the 36-year-old woman had died due to her infection with the virus in late September while a five-year-old who died this earlier week may have been the country's second victim of the disease.
"The H1N1 virus is responsible for the death of the 36-year-old patient," the University Clinic Essen in western Germany said in a statement, adding that she died two weeks ago due to "acute lung and multiple organ failure as a consequence of her infection".
The clinic called the woman a "high-risk patient" who was obese and, at the time of her hospitalisation, infected with the swine flu virus as well as several bacteria resistant to antibiotics.
"The experts now believe that the virus paved the way for the infection with these bacteria," it said. "Ultimately the complications of the viral infection led to the death of the patient."
The hospital said the dead patient was the second it had treated with the A(H1N1) virus. The first, a pregnant woman, was released after recovering from the infection.
"Thanks to extensive isolation measures, neither patients nor staff were endangered," it said.
The Robert Koch Institute (RKI), the national disease control and prevention agency, said the 36-year-old woman's case may have been the first of two fatalities "that could be linked to an infection with the new influenza ('swine flu')".
The five-year-old boy from the southern state of Bavaria who had been seriously ill for weeks died Tuesday of pneumonia. The RKI said the boy also tested positive for A(H1N1) although it may not have caused his death.
As of September 27, there had been more than 340,000 laboratory-confirmed cases of H1N1 and over 4,100 deaths, according to a World Health Organisation toll issued on Friday.
The WHO says that swine flu is about as lethal as an ordinary seasonal virus but cautions that the pathogen could mutate into a form that would make it more virulent.