Iran's mission at the United Nations has not yet responded to news of the prosecutors' complaint.
The move could lead to a deterioration in relations between the US government and American Muslims.
Members of the US Muslim community have already expressed concerns of a backlash after a deadly gun attack at the Fort Hood army base in Texas, which has been blamed on a Muslim soldier.
The mosques and the office building will stay open while the forfeiture case goes through court.
Prosecutors allege that the Alavi Foundation illegally funneled millions in rental income back to Iran's state-owned Bank Melli, through a front company known as Assa Corporation.
Bank Melli has been accused by the US Treasury of providing support for Iran's nuclear programme, which Washington says is aimed at building an atomic weapon.
Iran has denied those claims and insists that its nuclear programme is aimed at generating electricity.
US government officials have long alleged that the Alava Foundation was part of the Iranian government.
A 97-page complaint alleges that several senior Iranian officials are involved in the foundation, including the country's deputy prime minister and ambassadors to the UN.
"For two decades, the Alavi Foundation's affairs have been directed by various Iranian officials, including Iranian ambassadors to the United Nations, in violation of a series of American laws," Preet Bharara, a US attorney, said in a statement.
The New York office block, known as the Piaget building, was built in the 1970s, while the shah of Iran was in power.
Law and investment firms are among the companies using the building, which was valued at $570m to $650m in 2007.
The most recent US tax records show the Alavi Foundation earned $4.5m from rental of the building's offices in 2007.
If the office tower is forfeited, the foundation would find it hard to maintain support for the Islamic centres, which house schools and mosques.