The male tiger, which the local press identifies as "Altai", escaped its enclosure Saturday at the Cologne Zoo in western Germany and made its way to a nearby storage building.
Once there, the tiger attacked and killed its 43-year-old keeper, said police spokesman Stefan Kirchner, who added the animal's gate wasn't properly shut.
"This is the darkest day of my life," said zoo director Theo Pagel, who shot the four-year-old tiger with a rifle through the storage building's skylight.
The animal was killed before it could enter the visitor's area. No members of the public are believed to have witnessed the incident.
The woman's name has not yet been released.