Smolov scored after just nine minutes on his international debut in a 2-2 draw against the U.S in the southern city of Krasnodar on Wednesday, but his joy was short-lived as he had to be substituted.
"As I had feared (this part of) the season is over for me," the 22-year-old said on his Twitter feed following a medical on Thursday.
Smolov, who joined Anzhi on loan from Dynamo Moscow in July, told the club's website earlier on Thursday: "I felt a sharp pain while taking the shot... I think I'll miss at least two weeks."
He will miss Anzhi's Europa League tie next Thursday when the wealthy club from the volatile North Caucasus region could clinch a place in the knockout round if they beat Udinese at home as well as their final Group A encounter away to Swiss side Young Boys next month.
Guus Hiddink's team, who have assembled an expensive squad including Cameroon striker Samuel Eto'o, have excelled in their first European campaign. Anzhi top the group with seven points from four games, a point ahead of both Liverpool and Young Boys.
The Russian league season runs in two parts, from August to May with a three month mid-winter break from December to February.