Wright hosted the draw for next year's tournament at the Swiss Tech Convention Centre in Lausanne, Switzerland.
According to the Daily Mail, ex-football stars Leonardo Bonucci and Sami Khedira rushed to his aid after seeing Wright fall down a flight of stairs.
Medics are said to have given Wright an ice pack and it is understood he suffered no further injuries.
He managed to board a flight to Manchester as planned on Tuesday morning.
Wright underwent knee replacement surgery earlier this year.
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Some of those present at the event are said to have been surprised at how Wright was on his feet, given the relatively short time since his operation.
He broke the news of his operation by arriving at an episode of the Stick to Football podcast in a wheelchair.
His fellow pundit and ex-Manchester United captain Roy Keane wheeled him in and became his helper for the day.
Wright was also seen moving around on crutches.
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At the end of the episode Keane helps wheel him out, saying: "I've got you, I've got you. Team player."
"Jesus, I don't want this Roy," Wright protested as Jill Scott laughed.
"I'm his full-time carer," Keane added as Scott joked that it was like 'Little Britain'.
The pair have not always seen eye-to-eye with Wright admitting he previously held a grudge towards Keane over his jibe at Arsenal's lack of Premier League silverware compared to Manchester United.
"I see him as my friend now, but like I say, when we played I didn't like him, I didn't like him at all," said Wright.
"I remember when I won my Premier League medal when the camera came in I remember saying: 'Roy Keane, winner's medal'.
"Because Roy Keane one time said to me: 'Wrighty, you've got a cabinet full of losers' medals'.
"It's the kind of comment I would have said to him if the shoe was on the other foot but when he said it, it hurts you. I was laughing deep down because it's a killer, it finishes you, bam."
This isn't the first time Wright has gone under the knife for a knee problem.
In February 1998, aged 34, Wright had an operation on his left knee after tearing the cartilage.
The reigning champions England were drawn to face France, Wales and Netherlands at the tournament.
The draw means England's Dutch head coach, Sarina Wiegman, faces her native country.
The competition takes place next July in Switzerland.
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