The Catalan, participating in the Dakar for the second time, was involved in an incident a few kilometres from the end of the special stage from Al Henakiyah to Al Duwadimi on 8 January.
Falcon, 45, had received immediate assistance before he had to be airlifted to Al Duwadimi hospital for further treatment.
Falcón suffered a cerebral oedema due to the fracture of the C2 vertebra, as well as five ribs, the left wrist and the collarbone.
On Monday, his team announced the Spaniard had died.
“This Monday, January 15, Carles left us,” said the team in a statement. “The medical team has confirmed neurological damage caused by cardiorespiratory arrest at the time of the accident is irreversible.”
It added: “Carles was a smiling person, always active, who passionately enjoyed everything he did, especially motorcycles. He left us doing something that was his dream, racing the Dakar.
“He was enjoying himself, he was happy on the bike. We must remember him for his smile and for the happiness he generated in everyone.
“He was a computer engineer by training. Motorcycle instructor and motorcycle travel guide by passion. There are many who have learned at his side. He taught with patience, energy and happiness, he made everyone enjoy the bike.
“This is what he has left us and what we will always keep with us, all of us who have been close to him, family, friends, colleagues and fans.”
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