The club’s physiotherapist, Stijn Vandenbroucke, says the striker aggravated a hamstring injury during Saturday’s Russian Cup final.
He has recommended that the striker rests for a ‘few’ weeks.
Eto’o will fly to Cameroon on Monday so that the Indomitable Lions‘ medical team can examine the injury.
Cameroon are currently top of Group I on six points – just one ahead of Libya – while DR Congo have four and Togo just a single point so far.
Anzhi have offered to treat Eto’o back in Europe if Fecafoot are happy with the arrangement.
The striker played the full 120 minutes as his side lost on penalties to CSKA Moscow in the Russian Cup final.
His club commitments also meant he missed Cameroon’s goalless draw in Kiev against Ukraine, in what was Volker Finke‘s first match in charge of the Indomitable Lions.