Nicolás Ernesto Maduro Guerra, 29, known as Nicolasito, is a member of the pro-government Constituent Assembly.
Juan Guaidó, who is seen by the US as the country's legitimate leader, heads up a rival parliament that has been side-lined by the government.
The sanctions will freeze any US assets Nicolasito has and bars US firms and individuals from working with him.
Announcing the move on Friday, Treasury Secretary Steve Mnuchin said they were punishing him for serving his father's "illegitimate regime".
"Maduro's regime was built on fraudulent elections, and his inner circle lives in luxury off the proceeds of corruption while the Venezuelan people suffer," Mr Mnuchin said in a statement.
"Maduro relies on his son Nicolasito and others close to his authoritarian regime to maintain a stranglehold on the economy and suppress the people of Venezuela."
The statement also accused the president's son of engaging in propaganda and censorship on behalf of the government.
He joins dozens of other Venezuelans already under economic sanctions.
The US has been ramping up pressure since it recognised Juan Guaidó as the country's legitimate leader.
Since he declared himself interim president in January, Mr Guaidó has won the backing of more than 50 countries, but has struggled to take power.
Mr Maduro has largely retained the support of his military and key allies including Russia and China.
Earlier this week, the Venezuelan government claimed it had foiled an international-backed "fascist" plot to assassinate Mr Maduro - a claim Mr Guaidó dismissed.
Venezuela has been in severe economic crisis for several years - struggling with hyperinflation, high unemployment and chronic shortages of food and medicine.
Some four million people have fled the country since 2015, according to the UN.
More about: Venezuela