The call came after Ukraine accused Russian troops of killing dozens of civilians in the town of Bucha.
Russia is in its second year of a three-year term on the Geneva-based council.
A two-third majority vote by the 193-member assembly in New York can suspend a state from the council for persistently committing gross and systematic violations of human rights during its membership.
Speaking in Bucharest on Monday, Thomas-Greenfield said: "Russia's participation on the Human Rights Council is a farce.
"And it is wrong, which is why we believe it is time the UN General Assembly vote to remove them."
Since the Ukraine invasion began on February 24, the UN General Assembly has adopted two resolutions denouncing Russia with at least 140 yes votes. Moscow says it is carrying out a "special military operation" that aims to destroy Ukraine's military infrastructure.
"My message to those 140 countries who have courageously stood together is: the images out of Bucha and devastation across Ukraine require us to now match our words with action," Thomas-Greenfield, visiting Romania to see how the country is coping with an influx of Ukraine refugees, told reporters.
Bucha's deputy mayor said 50 of some 300 bodies found after Kremlin forces withdrew were the victims of extra-judicial killings carried out by Russian troops.
Reuters could not independently verify those figures or who was responsible for killing the dead residents.
Ukrainian authorities said they were investigating possible war crimes there, a description also used by French President Emmanuel Macron. The Kremlin categorically denied any accusations related to the murder of civilians in the town.
The United States has said war crimes have been committed in Ukraine and US experts were gathering evidence to prove it.
The General Assembly has previously suspended a country from the Human Rights Council. In March 2011, it unanimously suspended Libya because of violence against protesters by forces loyal to then leader Muammar Gaddafi.
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