His family and team-mates have been informed.
The fitness centre in east London was closed to the public for the rest of the evening, while police created a cordon around the venue as health and safety officers investigate.
A spokesman for the Met Police said it believed the dead man was struck by a metal pole, which was part of training facilities at the centre.
"The man was a competitor at the World Para Athletic Championships, being held in London. His next of kin have been informed."
Last September, Hayayei made his debut at the Rio 2016 Paralympic Games, finishing sixth in the javelin F34 and seventh in shot put F34.
London 2017 was to be Hayayei's second world championships. At the 2015 event in Doha, Qatar, he finished fifth in the discus F34 and eighth in shot put F34.
He was set to compete in the shot put, discus and javelin F34 events.
The sportman's family, who are in the United Arab Emirates, have been informed of his death and the UAE team were brought together at the team hotel to be told the tragic news.
During Friday's opening ceremony at the London Stadium, a moment of silence will be held in honour of Hayayei's death.
Tributes have been pouring in from across the sporting world this evening. Sir Philip Craven, president of the International Paralympic Committee, said his thoughts were with Hayayei's family.
"We are all truly devastated by this tragic news and the passing of Abdullah," he said. "The thoughts, prayers and condolences of the whole paralympic movement are with Abdullah's family, friends and team-mates, as well as the whole of the National Paralympic Committee of the UAE.
"We are all in state of shock at this terrible tragedy."
Ed Warner, co-chair of London 2017, said: "This is a devastating event, and everyone within the London 2017 Organising Committee is shocked and saddened.
"Our thoughts and prayers are with all of Abdullah's family and team-mates at what is undoubtedly a very difficult time for them. We will be working closely with all the competitors and teams over the days ahead to offer support wherever it is needed."
Newham Mayor Sir Robin Wales said: "The whole of Newham will be saddened by this tragic incident. All our thoughts, of course, are with the family of Abdullah Hayayei at this time."
IPC Athletes' Council chairwoman Chelsey Gotell added: "The IPC Athlete Council is devastated to hear about the passing of Abdullah Hayayei.
"As the Paralympic athlete community, we come together to celebrate the joy of sport, but we also come together as a family to mourn during the most difficult of times.
"On belief of all Paralympic athletes, we would like to extend our unwavering love and support to his family, team-mates, friends and the NPC of the United Arab Emirates."
