Getty images (2) Kelly Clarkson, Simon Cowell
Clarkson shared the news on Instagram with an "urgent memo" addressed to "everyone."
"My friend, Simon Cowell, is doing better now but was in an accident and won't be able to make Tuesday and Wednesday's live shows for AGT, but no worries America, someone far wiser, cooler and hotter is taking his seat!" Clarkson's memo said.
"The unbelievably amazing Kelly Clarkson," the memo added with a funny face emoji. "You're welcome in advance!"
Cowell, 60, was hospitalized on Saturday after falling off an electrical bicycle and landing on his back in Malibu, California.
The producer underwent a five-hour surgery Saturday night, a source told PEOPLE over the weekend, and "had to have a number of fusions and metal rod put into his back."
The source also told PEOPLE on Sunday that Cowell's "injuries are bad but he's also been told he was lucky."
The longtime TV judge is now recovering — and warned his fans to beware of electrical bikes on Twitter Sunday.
"Some good advice... If you buy an electric trail bike, read the manual before you ride it for the first time," Cowell said in a tweet. "I have broken part of my back. Thank you to everyone for your kind messages."
Trae Patton/NBC Simon Cowell
In an additional tweet, he added, "And a massive thank you to all the nurses and doctors. Some of the nicest people I have ever met. Stay safe everyone Simon."
AGT judges Sofia Vergara and Heidi Klum posted photos and videos from the Universal Studios stage on Sunday as the show continued taping without Cowell and shared their support for him on social media.
"We miss our boss!! Come back fast @simoncowell!!" the Vergara, 48, wrote on Instagram, sharing a photo with Klum and Howie Mandel gesturing to an empty chair.
"Wishing you a speedy recovery @simoncowell ❤️🙏🏻," Klum, 47, wrote.
On her Instagram Stories, Klum offered Cowell a get well soon message.
"Filming today for America's Got Talent and I'm here next to Simon's trailer," the model said in one clip. "I just wanted to say I miss you Simon and get well soon."
America's Got Talent airs Tuesdays and Wednesdays (at 8 p.m. ET) on NBC.