Hunt told the BBC late Thursday night that the move was unlikely to be a "magic wand" to get her released, but was an "important diplomatic step".
Asked if he was prepared to take Iran to international court, sanction it, or summon its ambassador, Hunt said: "All these things are possible, but we would like to solve this in an amicable way".
The development means the case will now be treated as a formal, legal dispute between Britain and Iran.
Zaghari-Ratcliffe was jailed in 2016 after being convicted of spying, which she has denied.
Iran refuses to recognise dual nationals, so it does not recognise Zaghari-Ratcliffe's right to be represented by the UK.
Diplomatic protection is a rare legal procedure in international law. States can use it to help one of its nationals whose rights have been breached in another country.
It is very different to diplomatic immunity, which is something given to diplomats to ensure their safe passage and protection from prosecution.
Meanwhile, Richard Ratcliffe, who has been campaigning for his wife's release and for the UK government to take this step, welcomed the news.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)