Dino 'Dappy' Contostavlos and Richard 'Fazer' Rawson were met by officers at a London airport after flying into the capital from Edinburgh.
"They were swearing at kids on the plane, being foul and threatening passengers," a source told The Sun.
"Cabin crew called ahead to the police, who were waiting when the plane landed. They were taken away by armed officers."
Contostavlos and Rawson were held for more than hour with friend DJ Mazer. Lead singer Tula 'Tulisa' Contostavlos was not involved.
A statement from the band read: "Fazer apologised on the plane at the end of the flight. They're sorry if their high spirits offended anyone."
N-Dubz release their new single 'Strong Again' on February 16.
> Click here to read our interview with the band