The Mehr news agency says they were involved in newsgathering, recruiting and training for Iranian journalists and had arranged trips abroad for them.
A BBC statement said no BBC Persian journalists were working inside Iran.
It said the reported arrests should be of deep concern to all those who believed in free and independent media.
On Friday, the BBC accused the Iranian authorities of intimidating those working for its Persian service.
‘Intimidation’
In a blog, the BBC’s Director General Mark Thompson wrote that the BBC had seen “disturbing new tactics”, including the targeting of family members of those working outside Iran.
The previous week, the sister of a BBC Persian staff member was detained and held in solitary confinement at a Tehran jail.
Iran accused the BBC of inciting unrest after the disputed re-election of President Mahmoud Ahmadinejad in 2009. Tehran also accuses the BBC of operating as a cover for the British intelligence service.
Last week, the BBC accused Iran of intimidating staff members of its Persian service by slandering them and arresting relatives.
BBC Persian broadcast online videos and interviewed protesters, who described deaths, injuries and arbitrary arrests carried out by security forces.
In his blog, Mr Thompson wrote that for BBC Persian staff, “interference and harassment from the Iranian authorities has become a challenging fact of life”.
“In recent months, we have witnessed increased levels of intimidation alongside disturbing new tactics,” he added.
