Rogozin was scheduled to meet with Moldovan President Igor Dodon in Chisinau on the latter's personal invitation, TASS reported.
The two planned to visit the city of Bender to attend official events on the occasion of the 25th peacekeeping operation in the Dniester area.
A spokesman for Romania's Ministry of Foreign Affairs confirmed that the plane with Rogozin on board was not permitted to cross the country's airspace.
Hungary, too, denied transit through its airspace and a stopover in Budapest, TASS said.
Read alsoEU ambassadors extend sanctions against Russians for 6 monthsRogozin's response to Bucharest's move was immediate. "The Romanian authorities have endangered the lives of passengers, women and children, flying by S7. Fuel was enough only until Minsk. You scumbags, retaliation will follow," he tweeted.
Румынские власти подвергли опасности жизни пассажиров рейсового самолета S7, женщин и детей. Топлива хватило до Минска. Ждите ответа, гады https://t.co/FC1C0wmBHp— Дмитрий Рогозин (@Rogozin) July 28, 2017
On March 17, 2014, the next day after Russia annexed Ukraine's Crimea, Rogozin became one of the first seven individuals who were placed by the then U.S. President Obama on the sanctions list. The sanctions froze his assets in the U.S. and barred him from entering the country.
He was also added to the Canadian and to the EU sanction lists due to the Crimean crisis.
Rogozin once stated that Russia's defense sector has "many other ways of travelling the world besides tourist visas" and "tanks don't need visas."