The official Granma newspaper said Castro flew out of Havana on Sunday, but did not reveal other details about his visit to the two countries, which are its most important trade partners in the region.
In Beijing, the Chinese foreign ministry confirmed that Castro would meet Hu during four days in Beijing, starting on Wednesday.
"Cuba is a major country in Latin America. It is also the first Latin American country to establish diplomatic ties with new China. China pays great attention to his state visit to China," said spokesman Liu Weimin.
Liu said the two delegations would sign cooperation documents, without giving details.
It is the first visit by Castro to either country since assuming power in 2008 from his brother, former president and revolutionary icon Fidel Castro, who is 85.
Raul Castro will be accompanied on his tour by Foreign Minister Bruno Rodriguez and Ricardo Cabrisas, vice chairman of Cuba's council of ministers, Granma said.
"These visits are of strategic importance, because China is one of the three main trading partners with Cuba," Juan Triana of the Center for the Study of the Cuban Economy told AFP.
"It is also important in these moments of great global difficulty to be able to explore whatever new business opportunities might exist with China and Vietnam," he said.
Vietnam is exporter of key agricultural products. It is Cuba's main supplier of rice, a staple food item on the island. According to official statistics, bilateral trade totaled $269 million in 2010.
The secretary general of Vietnam's Communist Party, Nguyen Phu Trong, visited Cuba in April.