The party took place in July 2020 when Buenos Aires was under a strict lockdown Mr Fernández himself had ordered.
At the time there was a ban on all gatherings, including funerals, and people had been told only to leave their homes if it was “essential”.
A judge has approved an “economic compensation” proposal agreed between the president and prosecutors.
The first couple paid the fine in the form of a charitable donation and legal proceedings against them were dropped.
The money will go to the Malbran Institute, a vaccine research body which has played a leading role during the pandemic.
Outrage spanned the political spectrum when images of the party emerged in August last year.
The scandal became known as “Olivosgate” after the name of the residence.
None of the people at the birthday party were wearing face masks.
Mr Fernández, a professor of criminal law, has said the party was “not a malicious act,” but admitted “recklessness and negligence”.
He called it an “error” and “slippage” during the “maelstrom” of managing a pandemic response.
The centre-left leader may have to take out a bank loan to pay the fine, according to some reports.
Guests at the party have also been charged, and are in negotiations with prosecutors to pay fines.