BEIJING—Yum Brands Inc.’s KFC is suing three companies in China for allegedly spreading rumors about the quality of its food, including that its chickens have eight legs, a move that comes as the fried-chicken company fights to regain lost ground in one of its most critical markets.

KFC said on its Chinese-language website that three Chinese media companies tarnished its image by spreading false information about its products on social media. KFC alleged in its statement that the companies spread rumors, “misleading the consumer,”...