"(President Nicolas) 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," Treasury Secretary Steven Mnuchin said in a statement on Friday.
Nicolasito, 29, is a member of the National Constituent Assembly, considered "illegitimate" by the US, and was designated by his father to be Director of the Inspectors Corps of the Presidency.
Mnuchin said that "Maduro's regime is built on fraudulent elections and his inner circle lives in luxury off the proceeds of corruption while the Venezuelan people suffer", Efe news reported.
"Treasury will continue to target complicit relatives," he added.
Washington's move freezes all the assets Nicolasito has under the US jurisdiction and bans all American organizations and companies from doing business with him.
The Venezuelan crisis is one of the issues on US President Donald Trump's agenda to discuss with other world leaders at the G20 Summit in Osaka, Japan.
Since coming to the White House in January 2017, the Trump government has stepped up the pressure on Caracas and applied economic penalties on over 100 Venezuelan officials and those in Maduro's inner circle, including his wife, First Lady Cilia Flores.
The US has also taken aim at Venezuela's principal source of income with tough sanctions on state oil company PDVSA, while revoking the visas of Venezuelan officials.
Venezuela is going through its worst political tension since January when Maduro was sworn in for another six-year term as Chief Executive, which was not accepted by the opposition nor by much of the international community.
In response, opposition leader and National Assembly Speaker Juan Guaido proclaimed himself as interim President of the country. The US was the first country to recognize Guaido as interim head of state and was later joined by some 50 other countries, most of them in Latin America.
( With inputs from IANS )