"We confirm that the plane was not allowed to fly over Romanian airspace," the foreign ministry told AFP.
The passenger aircraft, bound for Moldova's capital Chisinau, was forced to turn around and land in Minsk instead.
Bucharest acknowledged that the decision was made because of EU sanctions introduced in 2014 as the conflict surged between pro-Russian rebels and government forces in eastern Ukraine.
Rogozin is among dozens of Russian and Ukrainian individuals to have been hit by the punitive measures, which include asset freezes and travel bans.
After arriving in Minsk, the minister vented his anger at Romania's decision, saying the blockade was an unprecedented move.
"We have flown with the airline company several times before and never had any problems... With Belarussian, Polish, Slovakian and Hungarian airspace," Rogozin told the Russian Interfax news agency.
He later tweeted: "Expect a response, scoundrels!"
Rogozin had been on his way to Moldova, which is currently locked in a tug-of-war between the pro-Western government and Kremlin-friendly figurehead President Igor Dodon.
The small country wedged between Romania and Ukraine has an East-West cultural, linguistic and political split.
In May, Chisinau kicked out five Russian diplomats which saw Moscow turf out its officials in revenge.
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