The Argentinian footballer died in a plane crash in the Channel and never appeared for the Welsh team.
The crash happened on 21 January off the coast of Guernsey, killing Sala and pilot David Ibbotson.
FIFA, football's world governing body, said Cardiff must pay French club Nantes €6m "corresponding to the first instalment due in accordance with the transfer agreement".
Nantes had been due to get a £15m fee for Emiliano Sala - due in three instalments - and the clubs have been involved in a legal dispute.
Cardiff argued that Sala was not officially their player when he died and that therefore they were not liable for any of the fee.
Today's decision was made by FIFA's players' status committee.
In a statement, it said it "never lost sight of the specific and unique circumstances of this tragic situation during its deliberations on the dispute at stake".
Both clubs have the option to appeal against the decision to the Court of Arbitration for Sport.
It is not clear from FIFA's statement whether Cardiff will have to pay the other transfer instalments that were due.
The 28-year-old player was on a light aircraft travelling from France to Britain when the plane disappeared.
His body was eventually recovered but the body of the pilot has never been found.
Air accident investigators said they were exposed to harmful levels of carbon monoxide inside the cockpit before it crashed.
Earlier this month, a man and a woman were jailed for illegally accessing footage of Sala's post-mortem examination.