The Federal Department for Media Harmful to Young Persons said the disc merely contained political opinions, daily Süddeutsche Zeitung reported.
The department therefore found no basis on which to ban the disc, the report quoted director Elke Monsen-Engberding as saying.
The NPD is Germany's leading far-right party. It promotes an anti-immigrant agenda and is considered by the country's domestic intelligence agency to be a threat to the constitution.
On its website, the NPD welcomed the decision.
The party could "continue to try to transmit its ideas to young people, school children and first-time voters", NPD member Claus Cremer said.
NPD legal affairs minister Frank Schwerdt, who has served two prison sentences for inciting racial hatred and distributing Nazi propaganda, also appeared on the website celebrating the decision.
According to the NPD, the original demand to ban distribution of the CD came from the north-east state of Lower Saxony.
In November last year, German authorities banned the sale of home-grown hard rock group Rammstein's new album to fans under 18, for what it deemed explicit sadomasochist lyrics.