SOHR said Hoffmann, 19, was the third foreign fighter and the first female foreign fighter killed while fighting ISIL. The previous deaths of British and Australian nationals occurred over the course of the last two weeks.
The observatory reported a total of three skirmishes between YPG and ISIL in the vicinity of the northeastern Hasakah region of Syria on Sunday. It did not report the overall number of casualties sustained by the liberation forces.
On Sunday, French Prime Minister Manuel Valls said some 3,000 Europeans had joined Islamic State so far, and warned that the figure may reach 10,000 by year-end.
Islamic State have been thrust into the spotlight for violence against national and religious minorities, killings, abductions and the defiling of religious and historic buildings.