Joachim, who arrived at the end of May, admitted the offence after website El Confidencial broke the story.
The fine was “for breaking confinement, which he has recognised, he's been notified and €10,400 are required”, the official said.
The website leaked a report from the regional health authority that “a person who had travelled from Belgium … met a total of 27 friends and acquaintances on May 26 at a Cordoba residential building”.
Gatherings of no more than 15 people were allowed in the southern area under measures imposed to fight the pandemic.
Two days after the party, the same person from Belgium tested positive for coronavirus, the report said.
The 28-year-old prince, a nephew of the Belgian king, has 15 days to appeal the fine.
Spain has suffered more than 27,000 coronavirus fatalities and imposed strict lockdown rules which are due to be fully lifted at the end of the month.