Ms Saberi remained in the country to continue academic studies
Iran has accused an Iranian-American journalist, who formerly worked for the BBC, for operating illegally there.
Roxana Saberi is thought to have been arrested in January, although officials have not confirmed she is in prison.
She called her father in the US two weeks after her arrest to say she was being held for purchasing alcohol.
In recent years a number of joint US-Iranian citizens have been detained, accused of plotting a so-called velvet revolution in the Islamic Republic.
Ms Saberi, 31, worked briefly for the BBC three years ago, before her Iranian press credentials were revoked.
Ms Saberi's father, Reza, who lives in the United States, says she called him on 10 February to say she had been arrested for buying wine.
The BBC's Jon Leyne in Tehran says it is unusual to be jailed for more than a few days for such an offence.
Last week, when Ms Saberi had still not been freed, her father made the case public, though it was not confirmed by the authorities until Monday.
Foreign ministry spokesman Hassan Ghashghavi said the case was now in the hands of the justice ministry.
"Since 2006 when her press accreditation was revoked, she should not have illegally sought to gather information and news in Iran," he said.
Ms Saberi has also worked for the American public radio network NPR and the TV network Fox News.
Although Ms Saberi has Iranian and US citizenship the Iranian authorities do not recognise dual nationality, and our correspondent says they view many Iranian-Americans with suspicion.
NPR reportedly acknowledged that Ms Saberi's press credentials had been revoked but the authorities had continued to allow her to report short news stories.
Mr Saberi said his daughter had stayed on in Tehran after losing her accreditation to pursue a master's degree and do research for a book.
Iran and the US have not had diplomatic ties since 1979. Their relations are generally strained, with differences particularly sharp over Iran's nuclear programme and the US military involvement in the Middle East.