Mizan news agency quoted Tehran prosecutor Abbas Jafari Dolatabadi announcing the sentencing, though he did not elaborate on what the charges entailed.
However, there is no known case of a British-Iranian national being sentenced to six years in prison, suggesting this is a new case.
The British Foreign Office said in a statement early Monday it was "currently investigating the reported sentencing," without elaborating.
A number of dual nationals with Western ties have been arrested since Iran's 2015 nuclear deal with world powers.
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A UN panel in September described "an emerging pattern involving the arbitrary deprivation of liberty of dual nationals" in Iran, which Tehran denies.
Iran does not recognize dual nationalities, so those detainees cannot receive consular assistance.
Others with ties to the West detained in Iran include Nazanin Zaghari-Ratcliffe, a British-Iranian woman serving a five-year prison sentence for allegedly planning the "soft toppling" of Iran's government while traveling with her young daughter.
Her family says Zaghari-Ratcliffe remains held as Britain negotiates a settlement with Iran over 400 million pounds ($530 million) held by London, a payment the late Iranian Shah Mohammad Reza Pahlavi made for Chieftain tanks that were never delivered.