The Russian government gave the US until 1 October to close the mission.
USAID has worked in Russia for two decades, spending nearly $3bn on democracy and other programmes.
Correspondents say the government’s antipathy towards pro-democracy groups may be to blame for the move.
The Russian authorities have become increasingly suspicious of non-governmental organisations (NGOs), which it believes are using foreign funding to foment political unrest.
Earlier this year, President Vladimir Putin alleged that protests surrounding his re-election were orchestrated by US-funded NGOs.
Among the groups likely to be affected is Golos, whose exposure of electoral fraud at last year’s parliamentary elections helped spark huge anti-Kremlin street demonstrations.
Golos is partly funded by USAID.
In announcing the closure of the USAID office, US state department spokesperson Victoria Nuland said: “We remain committed to supporting democracy, human rights, and the development of a more robust civil society in Russia and look forward to continuing our cooperation with Russian non-governmental organizations.”
She would not be drawn on the reasons behind the Kremlin’s decision, but said there was a sense “that they don’t need this anymore”.
The United States began its operations in Russia after the end of the Soviet Union, spending around $2.7 billion on a wide range of human rights, civil society, health and environmental programmes.
USAID was due to spend around $50 million on its work in Russia this year.
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