Hila Sedighi was arrested at Tehran's Imam Khomeini Airport as she returned from the United Arab Emirates where she has been living with her husband for the last three years.
Her arrest was the latest in a series of arrests of artists, journalists and US citizens as part of a crackdown on what authorities have called a Western "infiltration".
The clampdown follows a nuclear deal Iran signed with world powers in July, that hardliners fear may open Iranian society to what they see as corrupting Western influences.
The relative, who asked not to be identified, said Hila visited Iran regularly and was shocked to hear she had been sentenced in absentia. She has lodged an appeal against the in absentia conviction. Iranian officials have not commented on Sedighi's case. She has been sentenced by a court dealing with media and cultural issues, the relative said.
Sedighi was awarded the Hellman/Hammett prize for free expression by Human Rights Watch in 2012. Another Iranian recipient of that prize, journalist Isa Saharkhiz, was arrested in November.
Dozens of journalists, activists and artists have been arrested on charges such as publishing "propaganda" since October in an apparent crackdown on free expression and dissent ahead of next month's election of a parliament and an assembly that will choose the Supreme Leader's successor.
Hila Sedighi backed a reformist candidate in 2009's disputed presidential election and one of her poems was used as a campaign slogan by Mirhossein Mousavi who is now under house arrest.
After hardline incumbent Mahmoud Ahmadinejad was announced the winner of the election, demonstrators took to the streets claiming the election was fraudulent, and Sedighi recited poetry at the protests.
She was interrogated by the Intelligence Ministry a few times. In 2011 a Revolutionary Court convicted Sedighi to four months in prison, although the sentence was suspended for five years.