The amount corresponds to the first instalment of the 17 million-euro fee Cardiff had agreed to pay Nantes before Sala was died in a plane crash on January 21 while travelling to join his new club.
Cardiff had previously resolved not to pay any of the money even though the transfer had been completed before the accident.
The announcement from world football’s governing body followed a meeting by its Players’ Status Committee.
In a statement, FIFA said it had “never lost sight of the specific and unique circumstances of this tragic situation during its deliberations on the dispute at stake.”
Both clubs can appeal the decision to the Swiss-based Court of Arbitration for Sport.
Nantes had previously appealed in February over Cardiff’s failure to pay the 17 million euros they said was owed.
The plane Sala was travelling on came down in the English Channel on January 21 during a night-time flight.
His body was recovered, but that of the pilot, David Ibbotson, has never been found.
A report by Britain’s Air Accidents Investigation Branch in August said that Sala and the pilot were likely exposed to “potentially fatal” levels of carbon monoxide on the plane.
