Hamid Baeidinejad, Iran's ambassador to Britain, said in a tweet Friday that the British government's move violates worldwide law.
The UK's exercise of diplomatic protection sends a message to Iran that the UK considers Nazanin a British national, and will assert her legal rights under worldwide law.
Diplomatic protection is a formal state-to-state process under global law in which a state seeks protection and reparation for breaches of worldwide law committed by another state against one of its nationals.
"No government should use innocent individuals as pawns for diplomatic leverage so I call on Iran to release this innocent woman so she can be reunited with her family", he said.
Iran refuses to recognise dual nationals so does not recognise Mrs Zaghari-Ratcliffe's right to be represented by Britain.
Nazanin Zaghari-Ratcliffe, who worked as a project manager for the Thomson Reuters Foundation, was detained while she was with her young daughter after visiting family in Iran in April 2016, Reuters reports.
Britain has said that it will grant "diplomatic protection" to Nazanin Zaghari-Ratcliffe, a UK-Iranian dual citizen jailed in Tehran since 2016, citing a lack of due process and access to medical treatment.
"We renew our plea for the Iranian authorities to release Nazanin as soon as possible", the statement added.
But what diplomats hope is that it will focus minds in Tehran, not just in the foreign ministry but also among the hardliners whom officials believe will ultimately decide Mrs Zaghari-Ratcliffe's future. And today, her case is back on the news agenda, after the British government announced she has been granted diplomatic protection. The UK government, Thomson Reuters Foundation and Zaghari-Ratcliffe have denied the allegations.
Hunt said he had "not taken this decision lightly" but considered the "unacceptable treatment" Zaghari-Ratcliffe had experienced during her years in detention.
The most immediate objective is for the United Kingdom government to gain a private consular visit with Nazanin in prison, and ensure she receives access to independent medical treatment.
In January, the Guardian newspaper reported she had been denied medical attention for lumps in her breasts and refused neurological care for neck pains and numbness in her arms and legs, despite being referred by the prison doctor for specialist treatment for both.
The development means the case will now be treated as a formal, legal dispute between Britain and Iran.
'It also gives us more power to arrange a visit to Nazanin to check her medical needs are being met.
While Mr Hunt acknowledged the move was unlikely to be a "magic wand" that secures her immediate release, he said it escalated the UK's response to the situation. Her plight has been highlighted by an articulate campaign mounted by her husband Richard.