Video surveillance footage from the bus led to suspicion that he wanted to set fire to the vehicle, thereby injuring as many people as possible and potentially killing some.
Prosecutors later said he was refusing to speak with investigators.
German news channel Spiegel TV quoted the man's father as saying his son, who lived locally, suffered from psychological problems.
Police spokesman Duerk Duerbrook said the attack occurred in the Kuecknitz district of Luebeck, northeast of Hamburg.
"We have no indication that this was a terrorist act", she said.
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The circulation of vehicles was reestablished in the mid-afternoon after traffic had been blocked for several hours around the scene of the incident due to a suspicious abandoned backpack, which was found not to contain any explosive material.
Police tweeted that 10 people were hurt.
"The bus was full", the police said, appealing to passengers who fled the scene to contact them.
One eyewitness reportedly told Lübecker Nachrichten: "The passengers jumped off the bus and screamed".
The authorities on July 20 said there was no information on the motive for the attack on a local bus in the northern city of Luebeck. "For that reason we have, as the investigation now stands, no indications that there was a terrorist background to this act".
Twelve people, including the man driving the truck when it was hijacked, were killed.