The election of a constituent assembly on Sunday was held amid mass protests. At least 10 people were killed.
Mr Maduro said the poll was a "vote for the revolution", saying "sanctions from the empire don't scare me".
It is unclear whether the president holds investments in the US and Washington's action was likely to be seen as symbolic.
"The emperor Donald Trump took decisions against me that show his desperation and hate," President Maduro said in a televised speech on Monday.
"I don't obey orders from foreign governments and never will... Sanction me as you wish, but the Venezuelan people have decided to be free and I am the independent president of a free nation."
Venezuela's new constituent assembly will have the power to rewrite the constitution and disband the opposition-controlled National Assembly.
The opposition coalition, which boycotted the election, said 88% of voters had abstained. It has refused to recognise the poll. Electoral officials said the turnout was 41.5%.
Protesters have blocked a number of roads in the capital, Caracas.
A march scheduled for later on Monday to honour those killed on polling day appears to have been postponed until Wednesday, the day that the constituent assembly is due to meet.
Venezuela's attorney general, Luisa Ortega, a vocal critic of the Maduro government, called the vote an expression of "dictatorial ambition".
The US had previously warned that it would not recognise the election, with President Donald Trump vowing "strong and swift economic actions" if it went ahead.
The sanctions were announced in a statement by US Treasury Secretary Steven Mnuchin.
"Yesterday's illegitimate elections confirm that Maduro is a dictator who disregards the will of the Venezuelan people," he said.
"By sanctioning Maduro, the United States makes clear our opposition to the policies of his regime and our support for the people of Venezuela who seek to return their country to a full and prosperous democracy."
Mr Maduro is only the fourth foreign leader to be blacklisted in this way, Mr Mnuchin said.
US National Security Adviser HR McMaster said the Venezuelan leader had joined an "exclusive club" that also includes Syria's Bashar al-Assad, North Korea's Kim Jong-un, and Zimbabwe's President Robert Mugabe.
On 26 July, the US Treasury had imposed sanctions on 13 current and former Venezuelan officials in a bid to deter Mr Maduro from holding the poll.
Those targeted include the interior minister and the head of the army.
"Who do these imperialists in the United States think they are?" Mr Maduro said in response to these sanctions. "The government of the world?"
He called the sanctions "illegal, insolent and unprecedented".
International condemnation of the latest vote was widespread on Monday. The EU expressed "preoccupation for the fate of democracy in Venezuela", and said it doubted it could accept the results.
However, Russia, Cuba, Nicaragua and Bolivia have stood by Mr Maduro.
Venezuela's 30 million citizens are suffering through shortages of basic goods and medicines, as the country's weakened economy declines still further.
A wave of anti-government protests has left more than 120 people dead in four months.
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