Bahman Daroshafaei, 34, a translator and former BBC Persian service reporter, was detained Wednesday at his home, according to the opposition website Kaleme.com.
"His family went to Evin Prison today. They managed to talk to someone on the phone who said Bahman was in Evin, but he would not be able to contact his family for another week or so," said the friend, who was in direct touch with the family but declined to be identified.
Daroshafaei's family said they had not been informed what the charges against him might be.
Iranian Foreign Minister Mohammad Javad Zarif said in London Thursday that he did not know about the case.
Some opposition activists have suggested that Daroshafaei's arrest, on the eve of the first visit to Britain by an Iranian foreign minister in 12 years, might have been orchestrated by hard-liners to thwart an improvement in relations as Iran emerges from international isolation under the moderate government of President Hassan Rouhani.
After living in London for several years, Daroshafaei returned to Iran in 2014 to be near his family.
His friend said six plainclothes officers had arrested Daroshafaei at his home and confiscated his computer, hard drives and mobile phone.
A few of Daroshafaei's friends in Tehran and London said they had received messages on social media in the past few days purporting to come from him. One said that she had been hacked after clicking on a link she received from Daroshafaei's account.
Britain reopened its embassy in Tehran last year after Iran agreed with world powers to curb its nuclear program in return for a lifting of sanctions. It has made no comment about Daroshafaei's detention.
Another Iranian-British citizen, Kamal Foroughi, remains in detention after being arrested in 2011 while working in Tehran as a business consultant.