The Argentine died when the aircraft in which he was travelling from France to the UK to complete his move to the Welsh club crashed in the English Channel.
The Bluebirds had argued that they could not be held liable for the £15m fee because Sala had not registered as a Premier League player.
But Fifa’s player status committee has decided that they must pay the amount equivalent to the first instalment of that fee.
A statement from the committee read: “In a meeting held on 25 September, 2019, the Fifa players’ status committee established that Cardiff must pay Nantes the sum of €6,000,000, corresponding to the first instalment due in accordance with the transfer agreement concluded between the parties on 19 January, 2019 for the transfer of the late Emiliano Sala from Nantes to Cardiff.
“The Fifa players’ status committee, which never lost sight of the specific and unique circumstances of this tragic situation during its deliberations on the dispute at stake, refrained from imposing procedural costs on the parties.
“The findings of the decision were notified to the parties concerned today. Within a deadline of ten days, Cardiff and Nantes can request a copy of the grounds of the decision, which can be appealed to the Court of Arbitration for Sport in Lausanne.”
The aircraft carrying Sala and British pilot David Ibbotson crashed on 21 January.
The body of Sala was recovered and he was formally identified by Dorset Police in February.
It is understood Cardiff were prepared to appeal the verdict at the Court of Arbitration for Sport if they were ordered to pay a fee.
A report from the Air Accidents Investigation Branch (AAIB) which was published in August found that Sala had a high concentration of carbon monoxide in his bloodstream prior to the plane crash.
Cardiff said they would require further clarification before deciding whether or not to appeal against the decision. A statement from the Welsh club read: “Cardiff City FC acknowledges the decision announced today by Fifa’s players’ status committee regarding the transfer of Emiliano Sala.
“We will be seeking further clarification from Fifa on the exact meaning of their statement in order to make an informed decision on our next steps.”
It has been reported that the findings mean Cardiff will also be liable for the other future instalments agreed between the clubs, but Fifa insisted that it could not comment on that possibility for “confidentiality reasons”.
“As mentioned in the media release, the sum of €6m corresponds to the first instalment currently due in accordance with the contract,” a spokesman for the world governing body said.
“For confidentiality reasons, we cannot comment at this stage on potential future instalments or other conditions of the transfer agreement.”