Police said that someone opened fire from a passing car and witnesses spoke of up to a dozen shots being fired close to the main police station.
"Nothing is known about the culprits yet but we can guess that this involves local crime gangs," investigators told German media.
The suspects fled and the area was quickly cordoned off.
The shots were fired in Friedrich-Stoltze Square, a busy area of bars and cafes, as local people enjoyed the Ascension Day holiday in the sunshine.

8 February 2017 Last updated at 11:58 GMT
An accident in Dumfries and Galloway has highlighted the perils of delivering huge wind turbine parts on country roads.
Two such deliveries recently have had very different outcomes.
One driver managed to successfully navigate Bargrennan Bridge, near Newton Stewart, in November.
But a delivery on the A713 on Tuesday saw a lorry and its giant cargo end up in a ditch.
At least three people were wounded, two seriously, when shots were fired in the German city of Frankfurt on Thursday.
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Footage of Bargrennan Bridge: Dabby McCreadie