A 20-year-old Syrian man was arrested on Tuesday evening and is believed to have an Islamist background, federal prosecutors in the city of Karlsruhe said.
The suspect allegedly attacked the two tourists, who had travelled together from North Rhine-Westphalia, on October 4th.
One of them, a 55-year-old man, later died from his injuries in hospital. The other, aged 53, survived with serious injuries.
The suspect has a long criminal record including charges of soliciting support for a foreign terrorist organisation, obtaining instructions to commit a serious act of violence endangering the state, bodily injury and threats.
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Police and the public prosecutor's office in Dresden reported that the examination of evidence had led to the Syrian man.
“Islamist terror is an ongoing major threat to our society, which we must fight against with all our might,” Justice Minister Christine Lambrecht said.
According to a report in the Bild tabloid, the Syrian man's DNA was detected on the knife, which police found near the scene of the crime in the city centre.
The suspect's DNA was already stored in police databases, the report said.
People with ties to Islamist extremism have committed several violent attacks in Germany, the deadliest being a truck rampage at a Berlin Christmas market in December 2016 that killed 12 people.
The Tunisian attacker, a failed asylum seeker, was a supporter of the Islamic State jihadist group.
Since 2013, the number of Islamists considered dangerous in Germany has increased fivefold to 680, according to security services.