The 29-year-old, who has been with the Seagulls since 2015, was forced out of Saturday's 3-2 friendly defeat to Atletico Madrid with a leg problem.
Boss Chris Hughton has now conformed that the Israeli international suffered a small fracture to his tibia and has already had an operation on the injury.
Kayal has made a total of 82 appearances in all competitions for the south-coast outfit, netting four goals in the process, but he will play no part in proceedings until November.
"It was operated on today and we expect him to be out for a period of 10-12 weeks," said Hughton. "The good news is that it was a clean injury and the operation went very, very well, so we don't expect any complications."
Brighton broke their transfer record on Monday with the capture of Davy Propper from PSV Eindhoven and that now seems a good move given the news on Kayal.