The woman was released and is reported to have minor injuries, while the man was taken to hospital in a serious condition. Police said there was no immediate suspicion of a link to terrorism.
Heavily armed police now surround the station, which has been evacuated and closed off to the public.
No information as to the suspect's identity or motive was provided by police.
Cologne train station, one of the biggest in the country, was evacuated and cordoned off. Police urged locals to avoid the area and warned of likely disruptions to train services.
"We're doing everything to get the hostage out of there unharmed", Gilles said.
German police 'not ruling out terror' motive in Cologne hostage-taking
German railroad operator Deutsche Bahn said all train traffic at the station was shut down.
Reports speak of at least one explosion during the incident. Ambulances and heavily-armed police were lined up and waiting behind the train station.
A woman held hostage by the perpetrator was only "lightly wounded", police tweeted shortly after she was freed around 3:00 pm (1300 GMT).
It wasn't immediately clear how the man was injured and police said on Twitter that emergency personnel were trying to revive him with CPR.
The attacker had to be resuscitated and was in intensive care for "extremely serious" injuries sustained when officers stormed the shop, they added.
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