The headquarters of an ethnic-Hungarian cultural association (KMKSZ) was set on fire overnight in Uzhhorod, capital of the Transcarpathia region, according to Hungarian news agency MTI.
Unidentified attackers threw a petrol bomb into the building which burnt out most of the ground floor, said MTI. No injuries were reported.
The building also suffered minor damage in an attack earlier this month.
"Extremist political views" are gaining ground in Ukraine and intimidating ethnic Hungarians, Hungary's Foreign Minister Peter Szijjarto told public television channel M1.
"All of this is unacceptable," Mr Szijjarto said, adding that he had summoned Ukraine's ambassador in Budapest.
More than 100,000 ethnic Hungarians live in Transcarpathia, mostly in towns and villages close to the Hungarian border.
The attacks come as the two countries remain at odds over an education law passed by Kiev last September that Budapest says restricts the right of the Hungarian ethnic minority to learn in their native language.
According to Kiev the law is about ensuring that all Ukrainian citizens can speak the state's official language, and it denies that the law is discriminatory.
Kiev has also criticised moves by Budapest to block cooperation between Ukraine and both the European Union and NATO until the dispute is resolved.
If Ukraine is serious about deepening its ties with the EU and NATO, it must be able to "keep extremists at bay," Mr Szijjarto said.
Some analysts in Ukraine have accused Hungary of acting in the interest of Russia, whose President Vladimir Putin is regularly hosted in Budapest by Hungarian premier Viktor Orban.
Ukrainian ultra-nationalists, who marched through a mainly ethnic-Hungarian town in Transcarpathia last year, said that Hungary's tough line on the education law is stoking separatist sentiment.
Pavlo Klimkin, Ukraine's foreign minister, on Tuesday said on Twitter that he "resolutely condemned" the arson attack in Uzhhorod, suggesting it was ordered from abroad.
The governor of Transcarpathia, Gennadi Moskal, went further, saying that the incident bore the hallmarks of the "Russian secret services".
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