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.
Image source: Wikimedia Commons President-elect Donald Trump celebrated his election victory at the Ultimate Fighting…
Millions of voters across the US chose to return Donald Trump to the White House…
Donald Trump declares victory in the US election as he addresses jubilant supporters in Florida.…
Stocks around the world are rising as Donald Trump appears to be on the cusp…
Donald Trump has won Pennsylvania, North Carolina and Georgia and taken a lead over Kamala…
Quincy Jones, the celebrated musician and producer who worked with Michael Jackson, Frank Sinatra, Ray…