The rouble-dollar rate reached 66.7 on the Moscow stock exchange. On Tuesday the rouble rate had been 63.4.
Sergei Skripal and his daughter Yulia were poisoned with the Russian nerve agent Novichok in Salisbury in March, though they have now recovered.
Russia denies any role in the attack.
The share values of major Russian firms, including Aeroflot, Rusal and Sberbank, also fell several percentage points in Moscow on Thursday.
A UK investigation blamed Russia for the Novichok attack. Mr Skripal and his daughter recovered after intensive care in hospital, and their current whereabouts are being kept secret.
Russia has criticised the new US sanctions as "draconian".
On Wednesday US state department spokeswoman Heather Nauert said it had been determined that Russia "has used chemical or biological weapons in violation of international law, or has used lethal chemical or biological weapons against its own nationals".
The British government has welcomed the move.
"The strong international response to the use of a chemical weapon on the streets of Salisbury sends an unequivocal message to Russia that its provocative, reckless behaviour will not go unchallenged," a UK Foreign Office statement said.
The Russian embassy in the US hit back on Thursday morning. Russia had become "accustomed to not hearing any facts or evidence", it said, adding: "We continue to strongly stand for an open and transparent investigation of the crime committed in Salisbury."
What are the sanctions?
The new sanctions will take effect on or around 22 August, and relate to exports of sensitive electronic components and other technologies that can have military applications. There will also be some further restrictions on Russian access to US financial services.
The state department says "more draconian" sanctions will follow within 90 days if Russia fails to give reliable assurances that it will no longer use chemical weapons and will allow on-site inspections by the United Nations.
The threatened measures include a far-reaching trade embargo on Russia - but excluding food - and a ban on Aeroflot flights to the US.
An official said it was only the third time that the US had determined a country had used chemical or biological weapons against its own nationals.
Previous occasions were against Syria and against North Korea for the assassination of Kim Jong-nam, the half brother of leader Kim Jong-un, who died when highly toxic VX nerve agent was rubbed on his face at Kuala Lumpur airport.
Are these the only US sanctions against Russia?
No. In June the US imposed sanctions on five Russian companies and three Russian individuals in response to alleged Russian cyber-attacks on the US.
All are prohibited from any transactions involving the US financial system.
Treasury Secretary Steven Mnuchin said the measures were to counter "malicious actors" working to "increase Russia's offensive cyber-capabilities".
The US and EU also have sanctions in place against dozens of Russian state officials and firms accused of involvement in the 2014 Russian annexation of Crimea and support for the separatist rebels in eastern Ukraine. Those sanctions restrict travel and financial transactions.
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