© picture-alliance/dpa/Kohls
The man was attacked in a street in the late afternoon, police said.
Witnesses called police after the attack, which occurred during a dispute. The victim succumbed to his injuries despite rescue efforts.
The suspect fled by bicycle.
Police later arrested a man following a widespread search. The suspect was due to be questioned on Thursday.
The attack happened in the Fasanenhof area of Stuttgart, a residential district in the city's south.
German tabloid Bild reported the victim was a German Kazakh.
Stuttgart is the capital of the southern German state of Baden-Württemberg, and is the sixth-largest city in Germany. It is very wealthy, with several major German companies headquartered there, including several major carmakers. It is generally regarded as one of Germany's safest cities.
Comment: While the cause of the dispute remains unknown, police have revealed that the 36-year-old German-Kazakh was killed by his 28-year-old Syrian roommate. "According to eyewitnesses, the two men were arguing, with the suspected assailant repeatedly asking the victim "Why have you done that?" after which he grabbed the sword and stabbed his roommate."