That development came amid unresolved US-Russian tensions, and tit-for-tat expulsions that earlier led Moscow to limit the number of US diplomatic staff in Russia.
The US visa move, in effect since October 12, prompted a heated rejoinder from Foreign Ministry spokeswoman Maria Zakharova.
American diplomats, she wrote on the Telegram platform, had long been "destroying" the consular services system in Russia, turning what should be a routine, technical procedure "into a real hell."
The State Department, for its part, pinned the blame squarely back on Moscow.
"The Russian government's decision to prohibit the United States from retaining, hiring or contracting Russian or third-country staff severely impacts our ability to provide consular services," a State Department spokesman said in a statement received by AFP.
"The extremely limited number of consular staff in Russia at this time does not allow us to provide routine visa or US citizen services."
It added: "We realize this is a significant change for visa applicants," and it cautioned them not to travel to Warsaw before booking an appointment with the embassy there.
The statement recognized that the shift to Warsaw, which took effect this month, was not an "ideal solution."
It added: "We considered a number of factors including proximity, availability of flights, convenience for applicants... the prevalence of Russian speakers among our locally engaged personnel, and the availability of staff."
Warsaw is around 1,200 kilometers (750 miles) from Moscow.
On the State Department website, Russia has been added to a short list of countries where "the United States has no consular representation or in which the political or security situation is tenuous or uncertain enough" to prevent consular staff from processing immigrant visa applications.
Most countries on that list have poor or no direct relations with the US, including Cuba, Iran, Syria, Yemen and Venezuela.
Amid a continuing dispute over how many diplomats each side can post in the other's country, Russia has placed the US on a list of "unfriendly" countries requiring approval to employ Russian nationals.
Russian applicants for nonimmigrant visas can still apply at any overseas US embassy or consulate so long as they are physically present in that country, the US statement said.
Meantime, the US Embassy in Moscow will be able to process only "diplomatic or official visas."
Successive rounds of tit-for-tat diplomatic expulsions by the two countries have left embassies and consulates badly understaffed, playing havoc with normal services.
This was a central subject of talks two weeks ago during a Russia visit by Victoria Nuland, the undersecretary of state for political affairs, but little progress was announced.
© 2021 AFP