The move comes as ties cool between Putin and US President Donald Trump, who has expressed mounting frustration at his Russian counterpart for refusing to accept a peace deal in Ukraine.
Trump scrapped plans for a peace summit with Putin last week, saying it would have been a "waste of time", and ruled out rescheduling unless the Russian leader sent signals he would agree to a deal.
The Plutonium Management and Disposition Agreement, signed in 2000 and amended in 2010, committed Moscow and Washington to reduce their vast Cold War-era stockpiles of plutonium by 34 metric tonnes each and use it for nuclear power instead.
US officials estimated the agreement would eliminate the material needed to produce the equivalent of around 17,000 nuclear weapons.
Putin had already suspended Russia's participation in the agreement in 2016, when ties were fraying with Trump's predecessor Barack Obama.
The law that Putin signed on Monday, approved by Russian lawmakers earlier this month, is a formal "denunciation" of the agreement.
Western leaders have accused Russia of nuclear sabre-rattling since it sent troops into Ukraine in February 2022.
Days after launching the offensive, Putin put his nuclear forces on high alert, and last year the Russian leader signed a decree lowering the threshold for using nuclear weapons.
On Sunday, Putin announced Russia had launched a successful final test of a new nuclear-powered cruise missile.
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