The Judiciary announced on Monday that a female Iranian national has been sentenced to 10 years in prison on charges of spying for Britain.
The person had been cooperating with the British espionage service and was tasked with designing, managing and planning cultural infiltration projects in Iran, said Esmaili.
The British Council is a cultural and educational organisation that operates overseas, but according to its website it is not "physically present" in Iran.
In March 2018, a London-based British council employee named Aras Amiri was arrested in Iran while visiting her ailing grandmother in her home country.
The organisation said it had not sent its employee to Iran on a work assignment.
Iranian authorities shut down the British Council's office in Tehran more than a decade ago for what Esmaili described as "illegal activities".
Ms Amiri has a fiancé based in the United Kingdom, who has been unable to get a visa to visit her in Iran since her arrest.
Esmaili said the woman had been in custody for nearly a year. However we have not been able to confirm that this is our colleague. He said the suspect had been jailed in Iran for the past year while her case was under investigation.
Mr Esmaili said such actions "drew the attention of Iran's security and intelligence services", which led to the woman's arrest a year ago.
Before her arrest, the 33-year-old Amiri had been living in London for 10 years - and had worked on cultural exchanges between Britain and Iran that included cooperation with Iran's Ministry of Culture. "We are in close contact with the Foreign and Commonwealth Office", the British Council said.
Iran is already holding British-Iranian national Nazanin Zaghari-Ratcliffe, who is in jail in Tehran for alleged sedition.
The UK is now engaged in a long-running effort to free Nazanin Zaghari-Ratcliffe, a dual British-Iranian national serving a five-year sentence in the Islamic Republic for alleged espionage.
Iran does not recognize dual nationality.
Iran offers Zaghari-Ratcliffe prisoner swap.
"Iran's security apparatus has apparently made the despicable decision to use these individuals as bargaining chips to resolve diplomatic disputes", she added.
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