The music mogul, 60, was trying out the bike in the courtyard of his Malibu home when he fell off.
A spokesperson for Cowell said he was due to have surgery on Saturday evening.
He is currently under observation in hospital and is said to be fine.
Cowell is the creator of America's Got Talent and serves as a judge on the show.
He has also been the judge on Britain's Got Talent, The X Factor and American Idol.
The spokesperson told Deadline: "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.
"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."
Cowell has a six-year-old son Eric with his partner Lauren Silverman.
Just last month, it emerged that Cowell had bought Sony Music Entertainment's stake in TV programmes including Britain's Got Talent and The X Factor.
The move sees him gain ownership of all the international versions of The X Factor and Got Talent programmes.
The Got Talent format airs in 76 markets, while The X Factor is broadcast in more than 130 territories.
Sony Music's share of the venture has transferred to Syco Entertainment, a company solely owned by Cowell.
Filming on the next stage of this year's Britain's Got Talent has been postponed because of the coronavirus
crisis but ITV has said it hopes to continue the series later this year.