"By sanctioning Maduro, the US makes clear our opposition to the policies of his regime," a statement by the US Treasury Department quoted Treasury Secretary Steven Mnuchin as saying on Monday, Xinhua news agency reported.
The statement also warned that anyone who participates in the ANC could be exposed to future US sanctions.
As a result of the sanctions, "all assets of Nicolas Maduro subject to US jurisdiction are frozen," said the statement, adding that US persons are prohibited from dealing with him.
Venezuela's Vice President Tareck El Aissami said on Sunday that voting was proceeding smoothly, except for an "isolated incident" in Tachira state that authorities brought under control.
He called Sunday's vote "a turning point towards a Venezuela with equality (and) social justice."
Samuel Moncada, Foreign Affairs Minister, said the participation of Venezuelans on Sunday, in the election of a National Constituent Assembly (ANC) is a "vote for peace".
After voting, the Venezuelan minister told the press of the importance to seeing the people out voting and rejected the country's critics.
"Opponents, some governments and even the CIA do not recognize this power... because they have a plan to control Venezuela. We do not need them or the vote of opponents," said Moncada.
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