Mr Rogozin earlier alleged that the Moldovan government was being controlled by a mafia oligarch.
Russia said Moldova's ban was "irresponsible", warning it would be followed by "an appropriate response".
Moldova's government seeks closer ties with the EU, but Russia sees the nation as part of its sphere of influence.
The situation became even more complicated after pro-Russian politician Igor Dodon became Moldova's president last December.
In May, Moldova expelled five Russian diplomats, without giving a reason.
Moscow threat as Moldova expels Russian diplomats
In a statement on Wednesday, Moldova's foreign ministry said it summoned the Russian ambassador to inform him that Mr Rogozin was now "undesirable person" in the country.
The ministry said it had to react after a recent interview on the Russian state-run Rossiya 24 TV channel, in which Mr Rogozin had made "defamatory criticisms of the Republic of Moldova and, implicitly, of the citizens of our country".
The interview was broadcast soon after the passenger plane Mr Rogozin was travelling on last week to Moldova was blocked by Romania from crossing its airspace.
Bucharest said it had acted because the deputy prime minister was under an EU travel ban over Russia's annexation of Ukraine's Crimea peninsula in 2014.
Ukraine has since banned direct flights flights to and from Russia, and Mr Rogozin's plane tried to fly over neighbouring Romania to reach Moldova.
In response to Moldova's move, Russia's foreign ministry summoned the Moldovan ambassador to "protest strongly" against "irresponsible acts" aimed at undermining bilateral relations.
In 2014, Moldova signed a far-reaching association agreement with the EU, and Russia promptly imposed import restrictions on the country's agricultural produce.
Russian troops are stationed in the breakaway Trans-Dniester region, which is economically dependent on Russia and defies the government in Chisinau.
In 2015, Moldova was rocked by a huge fraud case, when more than â‚¬1bn (Â£909m; $1.2bn) disappeared from three banks.
Moldova has declared Russian Deputy Prime Minister Dmitry Rogozin persona non grata over his "defamatory" remarks about the authorities in Chisinau.