The full-back fell awkwardly going for the ball in the first half of the match, and was stretchered off as Arsenal slumped to a 3-3 draw which hurt their hopes of securing Champions League football next term.
Arsenal manager Arsene Wenger confirmed the news after the match.
"It is broken fibula, the same leg," Wenger said, alluding to Sagna breaking the same leg early in the campaign. Sagna returned to first-team action at the end of January after a lengthy lay-off.
Wenger added: "He was kicked on it, it has not happened alone.
"When he was kicked, he has broken the leg.
"The guy closed him down and walked on him. I don't know if it was deliberate or not."