Conflicting reports said Ahmad either used a machete or kitchen knife to stab to death a 50-year-old man who is believed to be a German citizen. The 41-year-old man had been convicted in 2008 of planning an attack in Berlin against former Iraqi prime minister Iyad Allawi. At least one person was killed and four injured in the stabbing attack.
In December 2016, the Christmas market in Berlin was subjected to a terrorist attack in which a Tunisian national hijacked a truck and rammed it into a crowd, killing 12 people, and injuring many others. The suspect - who was covered in blood - was arrested a short time later.
Torsten Voss, Hamburg state's chief of the Constitutional Protection Office, said the suspect was one of 800 registered Islamists under observation in Hamburg, but that he was so far not linked to any extremist network.
Police said the suspect was 26 years old and born in the United Arab Emirates.
Officials wrote on Twitter that "the motive and the number of injured persons" were not yet known, but did confirm that "one person died". It was too soon to ascribe a motive to the attack, they said.
A 35-year-old bystander was also injured while trying to detain the suspect, police said.
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A friend had tipped authorities off to changes in the man, telling them he stopped drinking alcohol and started talking about the Koran, Torsten Voss, head of the Hamburg branch of the domestic intelligence agency, said. "First reports about a possible robbery can not be confirmed so far", he said.
Mr Scholz said the attacker had been due to be deported but that his expulsion had been delayed because he did not have identity papers.
The assault risks reopening a bitter debate over refugees two months before general elections, putting pressure on Chancellor Angela Merkel over her decision to open Germany's borders in 2015, letting more than a million asylum seekers in.
"The citizens who bravely helped to capture the perpetrator have my highest respect", Scholz said.
In both of these cases, the attackers had been asylum seekers.