The three-time Ballon d'Or winner will miss Tuesday's women's Nations League final second leg against Germany and several matches for her club in the weeks ahead.
Catalan media said Bonmati would be sidelined for "a minimum of two months" as she heals from the injury, which could rise above three months if she requires surgery.
The Spanish football federation said Bonmati finished the morning training session "in pain after a bad landing" during an accidental fall, before diagnosing her with "a fracture in her left fibula".
Bonmati started for Spain on Friday in a 0-0 draw against Germany in the first leg of the Nations League final.
She is set to miss upcoming Champions League games against Benfica and Paris FC in December, as well as the Spanish Super Cup in January and various Liga F matches.
Barca lead the league by six points ahead of Real Sociedad, while they are joint top of the Champions League league phase table with French giants Lyon.