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.
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)
