An initial police statement said that a man threatened police officers with a pickaxe and an “incendiary device”.
Later, a Hamburg police spokesperson told the BBC the suspect was armed with a pickaxe and had tried to ignite a petrol bomb – but that officers responded with pepper spray and then shot him.
He was given first aid at the scene and then taken to hospital.
“We are assuming that this is an isolated case, which means it is not football-related,” police spokeswoman Sandra Levgruen told reporters.
The incident is understood to have taken place at around 12:30 local time (10:30 GMT).
Video footage posted online, shows a man wielding an axe in front of police officers before a series of suspected gunshot sounds can be heard.
The man has not been identified by the police and the authorities have not commented on what motivations they believe were behind the incident.
Rory Smith, the New York Times’s chief soccer correspondent in Hamburg, said the incident took place on the Reeperbahn, a main street and nightlife area in the city just a few hundred yards from the Dutch fanzone.
BBC Sport journalist Gary Rose, who is also in Hamburg, said preparations were going ahead as planned for the match which kicked off at 15:00 local time.
The stadium is about five miles from the city centre where the incident happened.
There are approximately 30,000 Dutch fans in the city, and probably a similar number of Polish. There appears to be a good atmosphere ahead of the match, which is seemingly unaffected by the incident.