A man attacked passengers with a knife at a train station in the Munich area in southern Germany early on Tuesday, leaving four people with life-threatening injuries, Bavarian radio reported.
Police were checking witness statements that the man shouted "Allahu Akbar" (God is Great) during the attack, Bayerischer Rundfunk reported.
German media said police had arrested the perpetrator and that the victims were men. Police were not immediately reachable for comment when contacted by Reuters.
Germany, which is playing a supporting role in the fight against Islamic State, has not suffered a major attack by Islamist militants the like of which neighboring France and Belgium have experienced.