Officers searched 12 apartments in dawn raids, detained the suspects aged 16 to 21, and took them to a police station to record their personal details before releasing them, police in the port city said.
The group of local-area youths and adolescents, who were of German, Nigerian, Cameroonian and Turkish origin, were also suspected of having vandalised a nearby high school a day before the arson attack, police and prosecutors said in a joint statement.
The attack on the regional tabloid Hamburger Morgenpost, which caused property damage but no injuries, came just days after jihadist gunmen in Paris killed 12 people in the offices of Charlie Hebdo.
The perpetrators in Hamburg threw a manhole cover, several rocks and two incendiary devices into the building, causing damage to its archives.
The daily, known locally as the MOPO, had splashed the Charlie Hebdo cartoons on its front page with the headline "This much freedom must be possible!".
Prosecutors have refused to speculate on a motive for the newspaper attack, saying that with the aid of evidence collected in the raids, "we will now have to clarify this".