The two sides are expected to sign "important agreements", focusing on energy, trade and investment, Vietnam's government said in a statement late on Sunday.
Chinh is scheduled to meet counterpart Mikhail Mishustin and Russian President Vladimir Putin.
Chinh's visit comes as Vietnam has faced surging fuel prices since the U.S.-Israel war on Iran, with gasoline prices up 50% and diesel prices rising 70%.
Communist-run Vietnam maintains close ties with Russia, its longtime top supplier of military equipment, while Russian oil and gas companies operate offshore of Vietnam.
The two countries have been in talks for a Russian company to build Vietnam's first nuclear power plant, and officials said they are likely to officially sign a nuclear power agreement during Chinh's trip.