Just under 15 minutes of the Championship clash had been played when referee Peter Bankes halted proceedings, as stewards attended an incident in the Hammersmith End.
Medical staff from both teams assisted the paramedics on the scene, with the two teams taken off the pitch as the supporter continued to received attention.
The match got back underway about 40 minutes after it was stopped, with Fulham providing an update on the situation on social media.
“The supporter being attended to is being transferred to the hospital,” the club confirmed on Twitter.
“We’re sending our thoughts and best wishes for a full and speedy recovery. We will provide an update on the situation as soon as we have further information.”
It was not the only match to be delayed across the English divisions, with an emergency in the stands also resulting in Oldham’s League Two game with Rochdale being halted. Play resumed just over 20 minutes.
Oldham tweeted: “Our best wishes go with the Latics fan concerned. A heartfelt thank you to supporters who alerted it quickly to the stewards and medical team in the Main Stand Upper.
“We will try to provide a further update but he is back responsive and receiving treatment.”