It is the second time that the 29-year-old has suffered the injury this season, having missed several months of action after breaking a bone against Tottenham Hotspur last October.
"It is broken fibula, the same leg," manager Arsene Wenger told reporters. "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."
Sagna was widely tipped to be part of Laurent Blanc's squad for this summer's tournament in Ukraine and Poland.