The America’s Got Talent Host was testing the bike in the courtyard of his home when he fell.
Cowell, 60, underwent surgery on Saturday evening for his injuries, his spokesperson said.
He is currently under observation in hospital.
According to a spokesperson for the music mogul, Cowell is “doing fine”.
“Simon had a fall from his bike on Saturday afternoon whilst testing his new electric bike in the courtyard at his house in Malibu with his family,” his spokesperson told Deadline.
“He hurt his back and was taken to the hospital. He’s doing fine, he’s under observation and is in the best possible hands.”
Speaking on the Honest AF podcast, Osbourne said she believes her former X Factor and America’s Got Talent co-judge has “very dated” views.
“Simon doesn’t have an ability to see individuals,” said Osbourne. “He doesn’t like people who are overweight. Seriously.
“That’s why he turned down Jennifer Hudson, that’s why he wouldn’t champion her on American Idol. But it’s the truth. He’s very dated.”
Of her encounters with Cowell, Hudson previously said: “Simon told me I was ‘too big’ in every way. I think he meant my hair, my voice, my personality, my songs.”