"Raul Castro oversees a system that arbitrarily detains thousands of Cubans and currently holds more than 100 political prisoners," Pompeo said at United Nations headquarters in New York on Thursday, Efe news reported.
While the 88-year-old Raul stepped down as president in the spring of 2018, he remains the head of the ruling Communist Party.
"As First Secretary of Cuba's Armed Forces, Castro is responsible for Cuba's actions to prop up the former Maduro regime in Venezuela through violence, intimidation, and repression," Pompeo said.
Washington, which recognizes National Assembly speaker Juan Guaido as Venezuela's acting president, says that twice-elected leftist incumbent Nicolas Maduro is a dictator.
"In concert with Maduro's military and intelligence officers, members of the Cuban security forces have been involved in gross human rights violations and abuses in Venezuela, including torture," Washington's top diplomat said.
President Donald Trump's administration says that Cuba has soldiers and intelligence operatives are on the ground in Venezuela, something that Havana flatly denies, while the nearly 500,000-strong Venezuelan armed forces remain loyal to the Maduro government.
Pompeo imposed the sanction on Castro a day after Trump, meeting at the UN with the leaders of pro-US Latin American governments, said: "Maduro has sold out his nation to a foreign dictatorship."
Soon after taking office in January 2017, Trump moved to reverse the rapprochement with Cuba that began under his predecessor, Barack Obama.
And Washington has intensified pressure on Cuba amid Trump's growing frustration with the failure so far of the attempt to oust Maduro.
The administration maintains that Maduro is reliant on Havana to remain in power, even as Cuba depends on oil-rich Venezuela to meet its energy needs.
The travel ban applies to Raul Castro and to his four children: Alejandro, Deborah, Nilsa and Mariela.
Mariela Castro, an LGBT rights activist who runs the Cuban National Centre for Sex Education, visited the US in 2012 and 2013 to take part in conferences.
( With inputs from IANS )