Horrified witnesses saw the spectator fall around kick-off time and plunge towards the seats and concrete below.
A spokesperson from Wembley stadium confirmed the person had been taken to hospital in a serious condition.
One England fan said: “We saw his legs go over the barrier and then he fell and hit the ground and didn’t move.
“It seemed to take staff ages to get to him. One guy near us who saw the whole thing was crying his eyes out.”
Another England fan said: “I didn’t see it but spoke to some of the guys who did at half time. They were traumatised. He fell from the balcony towards the seats and the concrete.
“I think it happened around kick-off otherwise I would have noticed. That bit of seating was cleared.”
A Wembley stadium spokesperson said: “We can confirm that a spectator fell from the stands just after kick-off in the match between England and Croatia at Wembley Stadium.
“The spectator was given on-site medical attention and was then taken to hospital in a serious condition.
“We will continue to work with UEFA to ensure the matter is fully investigated and we are continuing to monitor the situation.”
England won the grudge match against Croatia with Raheem Sterling, recently made an MBE, scoring his first England goal at a major tournament at Wembley - the ground he dreamed of playing in as a local child.
Neeld Crescent, where he lived for five years, is within sight of the national stadium - with Mr Sterling also having a tattoo of the famous arches on his arm.
England manager Gareth Southgate insisted Sterling’s England record meant the Manchester City forward deserved his starting spot.
Southgate told the BBC: “Raheem has had this hex in the tournaments and not being able to get the goal, I felt he was dangerous all day, right from the start he was a thorn in their side. I’m really pleased for all of them.
“He is a good player, his goal-scoring record suggests we should have faith with him.”
The Danish football federation said the former Tottenham player is “stable” and set to remain in hospital.
In a statement on Twitter, the Danish FA said: “Latest news: This morning we have spoken to Christian Eriksen, who has sent his greetings to his teammates.”
After it was later confirmed Eriksen was stable, his team-mates agreed to resume the fixture in Copenhagen, with Finland claiming a 1-0 win thanks to Joel Pohjanpalo’s 59th-minute goal.