Hayayei, from the United Arab Emirates, made his debut in the javelin and shot put events at the 2016 Paralympic Games in Rio, finishing sixth in javelin.
He was pronounced dead at the scene after being attended to by emergency services at the Newham Leisure Centre.
"At this early stage it is believed the man was struck by a metal pole which formed part of training facilities at the centre," a spokesman for the Metropolitan police told British media.
UK public given route back to fitness through Team GB and ParalympicsGB programme Travel to Tokyo
IPC President Sir Philip Craven said: "We are all truly devastated by this tragic news and the passing of Abdullah. The thoughts, prayers and condolences of the whole Paralympic Movement are with Abdullah's family, friends and team mates."
Hayayei was preparing to compete in his second World Championships after finishing eighth in the shot put competition in the 2015 edition.
UK Athletics chairman Ed Warner said the organisation would provide any support the athletes needed to cope with the loss.
"This is a devastating event and everyone within the London 2017 Organising Committee is shocked and saddened," he said.
"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." (Reporting by Aditi Prakash in Bengaluru; Editing by Peter Rutherford; )
Olympic champion Lewis kick-starts nationwide 'art relay' to get the home fires burning for Tokyo
Houlihan claims she has been given a four-year ban because of a burrito