The measures, passed by 100 votes to nil, would ban foreign firms from doing business with the Iranian central bank.
Under the new sanctions, foreign banks that do business with Iran's central bank would be cut off from the US financial system.
The Senate's move came a day after the US Government said it is looking for new ways to impose fresh sanctions against Iran.
It also comes in the immediate aftermath of the attack on the British Embassy in Tehran following which Britain has recalled all its diplomats from Iran and has asked all Iranian diplomats from London to leave the country.
The US has been cautious about harsher sanctions, fearing such a move could disrupt the oil markets at a time of economic uncertainty for many Americans, and alienate potential allies.
But, Senators said that the sanctions were necessary to contain Iran's nuclear ambition.
"Iran's nuclear ambitions threaten the national security of the United States and its allies," said Senator Robert Menendez, in a statement.
The US and its Western allies have supported multiple rounds of sanctions on Iran, seeking to persuade it to curtail its nuclear work. Washington suspects Tehran of using its civilian nuclear programme to develop an atomic bomb, although Iran says its program is solely to produce electricity.