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.
At least three people were wounded, two seriously, when shots were fired in the German city of Frankfurt on Thursday.