The encounter at the Estadio Nuevo Mirandilla was halted around the 80th minute mark when the referee was alerted to a medical emergency in the stands.
Defibrillators were sent to the stands when it became apparent that the individual in question was suffering a cardiac arrest.
Play was stopped for more than an hour as players were sent back to their dressing rooms and the fan was treated at the grounds before being taken to hospital.
Cadiz provided an update on the situation after the game.
"When the 81st minute was completed, the match against Barcelona was paused as a result of a health alert in the south end stands," the statement read.
"The protocol established with the Red Cross quickly became operational, assisting a man in cardiac arrest.
"One of the medical teams with a defibrillator and monitor moved to the stands, beginning the resuscitation tasks. At the same time, Barcelona offered a second defibrillator in case its use was necessary, being moved to the area by the players themselves.
"The resuscitation was positive after a few minutes, and the fan was transferred to the ICU of the Puerta del Mar Hospital where he remains admitted.
"In addition, one of the Tribuna camera operators suffered a fainting spell that was also quickly treated by the stadium's medical staff without major consequences."
Barcelona won the game 4-0 to take top spot in La Liga, with goals coming from Frenkie De Jong, Robert Lewandowski, Ansu Fati and Ousmane Dembele.
