The car careened onto the pavement in the western city of Paderborn late Wednesday after a collision with another vehicle, striking the group of soldiers stationed at a nearby British military base, who were waiting at a crosswalk.
"Witnesses said the car ran a red light to enter the intersection," a police statement said.
A 20-year-old soldier succumbed to his injuries at the scene while a 23-year-old suffered life-threatening injuries. Four others were treated in hospital, two with serious injuries. The 21-year-old driver was also hurt.
Britain has about 20,000 soldiers based in Germany but plans to pull them out by 2020.