No other people were injured, a police spokesman said.
The attacker, who carried a rifle or “long gun”, acted alone and appeared to be a “disturbed man”, the interior minister of Hesse state, Peter Beuth, told the regional parliament.
Police have not identified the man or established his motive, spokesman Bernd Hochstaedter said, adding that nothing immediately pointed to him having a militant background.
German television showed pictures of heavily-armed police, wearing helmets and body armour, storming the Kinopolis complex in Viernheim, south of Frankfurt, and a couple fleeing the building.
Cinema employee Guri Blakaj told Reuters the gunman, who was aged about 18 to 25 and about 1.7m tall, entered the cinema at around 3pm and told workers to go into an office.
He then went into a cinema theatre. Blakaj, who said there were about six staff and 30 cinemagoers in the building, then heard shots fired.
Police special forces stormed the building and shot the gunman.
The identity and motive of the attacker remained unclear. A police spokesman said investigators found no identification documents with him.
There was still a heavy police presence at the scene into the late evening, and a helicopter circled overhead for several hours. Some 300 police officers and special forces were involved in the operation.
US President Barack Obama was briefed about the hostage situation at the cinema, the White House said. Spokesman Eric Schultz told reporters US officials were in contact with their German counterparts, but had no details. (Courtesy Reuters)