The 29-year-old, who joined Anzhi from Lokomotiv Moscow in January, will be out for up to eight months, the wealthy club from the volatile North Caucasus region said on their website.
Yeshchenko was injured in a 4-0 defeat at FK Krasnodar on Sunday when Anzhi also lost fellow Russia international Oleg Shatov, who will miss up to three weeks with a pulled hamstring.
Big spenders Anzhi, chasing their first Russian league title, are already missing several leading players, such as captain Samuel Eto'o, Brazilian playmaker Willian and Russia winger Yuri Zhirkov, through injury.
Sunday's defeat left Anzhi in third place, 10 points behind leaders CSKA Moscow with eight games remaining.
- Sports & Recreation
- Lokomotiv Moscow