The arrests were made the day after the BBC showed a documentary on Iran's supreme leader Ayatollah Khamenei. The BBC said the signal was disrupted in Iran.
The six filmmakers were not involved in the production, the BBC said Monday.
The BBC said it has no employees for the Persian service inside Iran.
"The individuals in question are independent documentary film-makers whose films have been screened in festivals and other venues internationally," the BBC said in a statement.
The BBC said the arrests were part of an ongoing Iranian government effort to put pressure on the broadcaster concerning its Farsi-language TV broadcasts.