The news corporation has said that Iran has stepped up a campaign of intimidation, including threats, arrests of relatives and travel bans.
The appeal will be made at a meeting of the UN Human Rights Council in Geneva.
The call for the appeal comes after the latest move by Iran to escalate its campaign against BBC Persian service journalists.
It has accused 152 current and former staff and contributors of "conspiracy against national security" and initiated criminal investigations.
Iran has also slapped an asset freeze on many of the journalists.
More than 20 Persian service journalists or family members have received death threats.
"The BBC is taking the unprecedented step of appealing to the United Nations because our own attempts to persuade the Iranian authorities to end their harassment have been completely ignored," said BBC Director General Tony Hall.
An estimated 18 million Iranians, a quarter of the population of Iran, regularly use the BBC's Persian service online, on radio or on satellite television. Some 12 million people regularly watch its TV programmes, which include news, current affairs and entertainment.
"Iranians are turning to BBC Persian in huge numbers because they cannot get reliable and impartial news and analysis from the Iranian media which is heavily censored," said Rozita Lotfi, head of BBC Persian.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)