Riding high in opinion polls, the populist party filed a 16-page claim against Interior Minister Johanna Mikl-Leitner of the conservative ÖVP party, as well as against Chancellor Werner Faymann and Defence Minister Gerald Klug, who belong to the Social Democrats (SPÖ).
In the claim submitted to prosecutors, the FPÖ accused the officials of "wilfully" breaking national immigration laws and helping to transport illegal migrants to the German border.
"Tens of thousands of people have been able to cross the border without restrictions since the beginning of September," FPÖ leader Heinz-Christian Strache told reporters in Vienna on Tuesday.
"The deliberate omission of controls... massively endangers the preservation of public order and security in Austria," he added, reiterating his call for a border fence.
The move came as neighbouring EU member Slovenia announced on Tuesday it would build "temporary barriers", potentially including fences, on its border with Croatia to help stem the flow of migrants.
Austria has become a key transit country for the migrants -- mainly from Syria, Afghanistan and Iraq -- desperately seeking to reach northern Europe through the Balkans before winter sets in.
Like other European far-right parties, the FPÖ has been steadily gaining support as the country faces a record 70,000 asylum claims so far this year amid Europe's worst migration crisis since World War II.
Recent national opinion polls have put the party in first place with more than 30 percent of voter intentions, although the next general elections are not due until 2018.
Austria's squabbling coalition government is expected to discuss border measures on Wednesday.
Faymann has repeatedly rejected the interior ministry's suggestion to build a fence to control the influx.