The male fan fell 15 feet and was taken to hospital with head and neck injuries.
Cardiff boss Dave Jones was concerned only about the fan not the entertaining 3-3 draw he had just witnessed.
He said: "I couldn't give two hoots about the result after that. One or two of the players saw it and Craig [Bellamy] said it made him feel physically sick.
"We don't know much about him but all we'll say is that we as a club send our best wishes for a speedy recovery.
"We desperately want to do well for our supporters and as a club we have a duty to them. At the moment, we are all just concerned about that guy."
Millwall boss Kenny Jackett also expressed his concern about the fan.
"We wish the lad well who fell from the stand. I didn't see it myself but Neil Harris did and said it wasn't good," he said.
A statement on the Millwall website read: "A male Cardiff fan climbed on to the yellow safety railing, lost his footing and fell into the low tier, some 15 feet.
"He received lengthy treatment by Millwall club doctors and the matchday medical team and was taken to Kings College Hospital by ambulance.
"He sustained head and neck injuries and is currently in a 'stable condition'. His next of kin have been informed.
"Police are investigating and the Health and Safety Executive have been informed."