The white van crashed into the glass facade of the building on the outskirts of Amsterdam around 0400 local time (0200 GMT), where it caught fire.
Police said no one was injured and the driver of the van who managed to get away and had not yet been found.
De Telegraaf is the largest daily in the Netherlands, specializing in sports and crime.
Last week, a rocket launcher was fired at an office housing several magazines in the same Amsterdam area. A 41-year-old man was arrested for that attack, in which no one got hurt.
More about: DeTelegraaf
