The party has campaigned heavily against letting migrants into the country, and won seats in parliament for the first time in 2016.
The party, known as Kotleba-People's Party Our Slovakia (LSNS), has campaigned heavily against letting migrants into the country, and won seats in parliament for the first time in March 2016.
It currently has 14 MPs sitting in the 150-member parliament.
"In the opinion of the prosecutor's office, the objective of this political party is to remove the current democratic system in the Slovak Republic," Andrea Predajnova, a spokeswoman for the prosecutor general, told AFP on Thursday.
Party chief Marian Kotleba, 40, is notorious for having led street marches with party members dressed in black neo-Nazi uniforms before he entered parliament.
Hostile to both Slovakia's sizable Roma minority and the established elite, he was repeatedly detained and charged with hate speech, chiefly against Roma, before becoming an MP.
Kotleba has also praised former Slovak president Jozef Tiso, who agreed to deport tens of thousands of Jews to Nazi Germany during World War II.
"A large amount of evidence proves that the Kotleba-People's Party Our Slovakia is an extremist political party with fascist tendencies that violate the constitution of the Slovak Republic, our laws and international treaties," Predajnova said.
Prosecutors had received around 170 formal complaints requesting that the party be banned, she added.
A spokesman for the Slovak parliament told AFP that LSNS deputies would be able to keep their seats regardless of a ban.
But with opinion polls ranking the LSNS as Slovakia's third most popular party -- the latest survey gives it 11.1 percent voter support -- analysts point to a potential backlash against a ban.
Prime Minister Robert Fico, a Social Democrat who is nonetheless staunchly anti-migrant, this month urged justice officials to take action against the party.
Kotleba, a former teacher, founded his first party, Slovenska Pospolitost (Slovak Brotherhood), in 2003 but it was banned by the interior ministry three years later for inciting racial, national and religious hatred.