Following on from weeks of speculation about the vote, which was narrowly won by independent Alexander Van der Bellen, the court's spokesperson confirmed via Twitter that it had received a complaint from FPO leader Heinz-Christian Strache.
"(The) challenge by Heinz-Christian Strache of the presidential run-off vote has arrived at the Constitutional Court," the tweet read.
The May presidential election was one of Austria's tightest, with Van der Bellen defeating FPO candidate Norbert Hofer by less than one percentage point, with the difference thought to be about 31,000 votes.
While preliminary polls put Hofer slightly ahead, it was reported that postal votes gave Van der Bellen the edge.
The FPO has since complained about certain aspects of the election, particularly in regards to postal votes, with FPO leader Strache saying there was "diverse information" relating to possible irregularities.
While the position of president is largely ceremonial in Austria, Hofer would have become the first far-right head of state of the European Union.
Austria far right party challenges presidential election defeat, says its candidate "could have become president" #bpwahl16— Anthony Mills (@AAMills) June 8, 2016
Commentators reported that Van der Bellen's narrow victory saved Austria and the EU from a political earthquake, as the FPO's Euroskeptic and anti-immigrant sentiment directly contradicts the views of the establishment in Brussels.
However, in regards to the latest legal challenge, once it has been filed, the constitutional court must decide on the validity of the claims.
For the case to continue, the court would have to find that a law was broken that might have affected the election's outcome.