Under the sanctions, US firms and individuals are banned from doing business with Mr Maduro.
The election on Sunday was marred by violence, with widespread protests and at least 10 people killed.
President Maduro hailed the poll as a "vote for the revolution".
The opposition coalition, which boycotted the election, said 88% of voters had abstained. It has refused to recognise the election, and called for more protests later on Monday.
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."
On 26 July, the US Treasury 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. "The government of the world?"
He also called the sanctions "illegal, insolent and unprecedented".