The motives of the man are still unclear.The incident took place near a doner kebab stand at Listplatz square, Germany's Bild Reports.
The perpetrator has been arrested by police, German media report, citing eye witnesses.
Photos posted on social media show the alleged perpetrator lying on the ground, restrained by police officers.
Police have confirmed that the man was arrested after he had used a machete to kill a woman and injure two more people in Reutlingen.The perpetrator was acting alone, police said, adding that there is no evidence suggesting that he had any accomplices.
The attack comes two days after a gunman killed nine people and injured over 30 in a shopping mall shooting spree in Munich.
Comment: Germany: Refugee injures 4 in grisly axe attack before being killed by police