FBI spokesman Greg Comcowich says the man's name is not being released until he appears in court because the case involves a juvenile.
Comcowich would not say in what town the man was arrested.
He says the arrest was made in coordination with state and local police from New Jersey and Rhode Island.
Authorities issued an Amber Alert for the Portsmouth girl after she was reported missing by her mother Wednesday morning.
Police say a witness saw someone matching the girl's description leave home with a man.