REUTLINGEN, Germany—A Syrian man used a long knife to kill a woman here on Sunday in an apparent personal dispute, and injured two other people before being detained, police said.

The suspect is a 21-year-old asylum seeker from Syria, the police said. The man was known to the police and had been charged in the past with assault.

The incident quickly made national news in a country on edge in the wake of a spate of violence across Europe that has fanned fears of a rising terror threat. Another asylum seeker, registered as a 17-year-old Afghan, injured five people in an ax attack last Monday in Würzburg, a two-hour drive from here.

But unlike the Würzburg assault, in which Islamic State claimed responsibility, the Reutlingen incident appeared to be the result of a personal dispute, police said.

“There is no evidence that it was religious or terrorist-motivated,” a police spokesman said.