Peter Beuth told the state of Hessen's parliament that police stormed the Kinopolis complex in Viernheim, near Frankfurt, after shots were reported.
"The police thought that the gunman was holding hostages and because of that he was shot dead," he added.
At least 20 people are said to have been hurt.
Most were apparently suffering the effects of tear gas released as police stormed the complex. It is not clear whether anyone was wounded by the attacker.
Heavily armed police surrounded the complex after the incident began.
The Frankfurter Allgemeine newspaper said it was unclear if there was a political or ideological motive, or if it was an attempted robbery.
Mr Beuth also said: "The police had an emergency call at 2:45pm [12:45 GMT]. The caller said there was a masked man... armed with a long gun. It is unclear whether it was a real gun.
"The caller heard four shots and said that the masked man appeared a little mentally unstable. Police special forces were called."