Iran officials say five people were convicted and sentenced for "cooperating with Iran's enemies," a government euphemism that usually implies cooperating with the United States.
Siamak Namazi was arrested nearly a year ago and became the first US citizen reported to have been detained in the country since the announcement of the Iranian nuclear program deal.
The agreement was hailed by US President Barack Obama as a way to impede Iran from obtaining a nuclear weapon.
The sentence comes after four US prisoners were released by Iran earlier this year as part of a US-Iran prisoner swap that granted clemency to seven Iranians indicted or imprisoned in the United States.
Washington Post journalist Jason Rezaian, Marine veteran Amir Hekmati and Christian pastor Saeed Abedini were three of the four freed in the swap.
Siamak Namazi is a Dubai-based businessman with dual US and Iranian citizenship. His father, Baquer, was detained in February 2016.
The International Campaign for Human Rights in Iran said the country does not recognize dual citizenship and that it "routinely harasses citizens and dual nationals with trumped up national security charges."
The human rights group told CNN in September that it was aware of several dual nationals imprisoned in Iran when commenting on the five-year sentence of a British-Iranian woman whom Iran's Islamic Revolutionary Guard Corps accused of attempting to overthrow the government.
The US State Department released a statement Tuesday calling for the immediate release of father and son.
"We join recent calls by international organizations and UN human rights experts for the immediate release of all US citizens unjustly detained in Iran, including Siamak and Baquer Namazi, so that they can return to their families," the statement read.
Baquer Namazi has a US passport with his birthplace listed as Iraq. According to the US State Department, he is a former UNICEF employee whose health is being reported as "declining."
Iranian officials were not clear who has to pay the $4.8 million fine but said the amount is what the convicted "had received from the US for their mission in Iran."
Iranian news agency IRIB said the five sentenced were paid by the United States for "anti-Iran activities."
Under Iranian law, the convicted have 21 days to appeal their sentence.