The club confirmed that a man in row one, block 126 of the Amsterdam ArenA fell five meters in the 39th minute and was immediately rushed to the hospital.
"He was taken to hospital with serious injuries," read a message on Ajax's official Twitter feed.
Speculation spread on social media sites that the supporter had died as a result of the injuries but the Amsterdam police force vehemently denied the claims.
"No update about the fan who fell at the ArenA during Ajax-Barcelona," it stated. "Rumors that the fan has passed away are not correct."