The full-back pulled up during the second half of the 3-3 Barclays Premier League clash against Norwich at the Emirates Stadium.
Sagna had suffered a similar injury against Tottenham last October.
Arsenal boss Arsene Wenger said: "It is broken fibula, the same leg.
"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 dont know if it was deliberate or not."