The Senate also blamed the Saudi crown prince for the murder of journalist Jamal Khashoggi, a USA resident.
The Saudi foreign ministry described the move as "interference" based on "untrue allegations".
However, it is seen as a rebuke to Donald Trump's Saudi policies.
The vote was held weeks after the Save the Children charity released an estimate that "since the start of the war in Yemen, some 85,000 infants and children under the age of five may have died of starvation or disease", as NPR reported. "Today we tell the despotic regime in Saudi Arabia that we will no longer be part of their military adventurism".
Khashoggi, a Washington Post journalist, was murdered in the Saudi consulate in Istanbul on October 2.
While Riyadh has lately responded belligerently to countries-Sweden and Canada are the latest victims of Riyadh's wrath-that have voiced concerns over Saudi Arabia's poor human rights record, the U.S. has not been subjected to the same abrasive rhetoric.
The Senate's position had been based on " unsubstantiated claims and allegations, and contained blatant interferences in the Kingdom's internal affairs, undermining the Kingdom's regional and worldwide role", a Saudi Foreign Ministry statement said.
Saudi Arabia's response came earlier today, with the kingdom adopting, for the first time, somewhat undiplomatic and disapproving language toward its staunch American ally.
The resolution passed by the US Senate last week states it "believes Crown Prince Mohammed bin Salman is responsible for the murder of Jamal Khashoggi" and "calls for the government of the Kingdom of Saudi Arabia to ensure appropriate accountability for all those responsible for Jamal Khashoggi's murder".
Canada is looking into ways to cancel a giant 2014 weapons deal with Saudi Arabia, Prime Minister Justin Trudeau said Sunday, as criticism mounts over the kingdom's role in the murder of journalist Jamal Khashoggi and the Riyadh-led war in Yemen. "By creating this rupture, the US Senate surely realizes who benefits from it. Iran, of course, our common enemy".
A non-binding resolution called upon Mr Trump to remove all U.S. forces engaging in hostilities in Yemen, except for those combating Islamist extremists. The Yemen war powers vote was far closer, with several Republicans joining Democrats in the 56-41 tally.
This represents the first time in US history the Senate has voted to withdraw military forces from an unauthorized war using the War Powers Resolution.
Saudi Arabia's public prosecutor has said Khashoggi was killed on the orders of a rogue intelligence officer. The calculation is that Crown Prince Mohammed bin Salman of Saudi Arabia may be willing to cut his losses and end the bombardment of the Middle East's poorest country.
His body has not yet been found.