He said authorities were still trying to determine the circumstances of the attack. Fourteen people were injured, two seriously.
The bus driver stopped immediately so the rest could escape.
Investigators said flammable liquid was found in the backpack but no explosives.
"There was an incident on a public bus in Luebeck Kuecknitz", said police in the state of Schleswig-Holstein, where Luebeck is located.More news: Vivo NEX India Launch
He then walked back to find out what was going on and was hit by the assailant, Hingst said.
In June, German police said they foiled what would have been the first biological attack with the arrest of a Tunisian suspected extremism in possession of the deal poison ricin and bomb-making material.
Five of the victims are still receiving hospital treatment.
The suspect is a 34-year-old man who lives locally.More news: MAC comments on Canada’s Cabinet shuffle
"The background to the crime is still unclear and the subject of the ongoing investigation", the police and prosecutor's office said in a statement.
"According to local reports, witnesses say the bus was packed with passengers when a man dropped a "smoldering backpack" and started attacking people".
"Luckily no-one was killed", said Luebeck chief prosecutor Ulla Hingst.
The bus was travelling from Luebeck to the neighbouring seaside resort of Travemuende, where an annual regatta, the Travemuender Woche, was opening later Friday.More news: New species of armoured dinosaur discovered in Utah