Three years ago Tamberi and Mutaz Barshim of Qatar, who had been friends and rivals for years, agreed to share gold after asking permission from the event officials.
On Sunday, however, Italian Tambiri posted a picture of himself in a hospital bed.
"Unbelievable... This can't be true," he said.
"Yesterday, two hours after I wrote 'I deserve it' on social media, I felt a stabbing pain in my side. Emergency room, CT scan, ultrasound, blood test. Probable kidney stone.
"And now I find myself, three days before the event for which I sacrificed everything, lying in a bed, helpless, with a fever of 38.8."
Tamberi said he had been advised to postpone his flight to Paris until tomorrow.
"Only one thing is certain, I don't know how I will get there, but I will be there on that platform and I will give my soul until the last jump, whatever my condition will be," he wrote.
Tamberi's preparations looked to be on course when he jumped a world leading 2.37 metres to win the European title in June, but he then picked up a minor thigh injury.
Barshim has also had injury problems, lengthening the odds on either man becoming the first to win two Olympic golds in the event that has been in every Olympics since 1896.
The qualifying competition is on Wednesday, with the final on Sunday.
Triathlon: Belgium out of relay after athlete falls ill
Belgium will not take part in the triathlon mixed relay event at the Paris Olympics on Monday after one of their athletes, Claire Michel, fell ill, the Belgian Olympic Committee (COIB) said on Sunday.
"Claire Michel, a member of the relay team, is unfortunately ill and must withdraw from the competition," the COIB said in a statement.
"The COIB and Belgian Triathlon hope that lessons will be learned for future triathlon competitions at the Olympic Games.
"We are thinking here of the guarantee of training days, competition days and the competition format, which must be clarified in advance to ensure that there is no uncertainty for athletes, entourage and supporters."
World triathlon said it had not heard from the Belgian team.
"The team has submitted their team declaration, chose their position on the pontoon this morning and checked-in their bikes also this morning. We have not received any other communication form them," a World Triathlon spokesperson said.
Training sessions for the swimming leg of the triathlon have been cancelled due to poor water quality in the River Seine and the men's event was put back to last Wednesday, taking place on the same day as the women's.
Organisers said on Sunday they were confident Monday's relay would take place despite cancelling Sunday's training.
Paris 2024 organisers did not immediately respond to a request for comment.
