The newspaper Hamburger Morgenpost said on its website the overnight arson attack destroyed several files in its archive, but didn't injure anyone.
Hamburg police said it had detained the two young men near the newspaper building.
Spokeswoman Karina Sadowsky didn't give any details about the men and said police were still investigating the incident.
The Hamburg tabloid newspaper published the Charlie Hebdo cartoons the day after the attack against the newspaper in Paris to express its solidarity with the slain journalists.
Several other national and local German newspapers also published the cartoons. They are now getting police protection.
