West Ham manager Bilic has revealed that the forward will be out for another eight weeks, until mid-February.
Senegal kick off their 2017 Afcon campaign on Sunday, January 15 in their first Group B game.
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They will do that without Sakho who has been ruled out of action for up to eight more weeks with a back injury.
The forward in November was initially ruled out for six weeks, meaning he could make the Afcon.
West Ham manager Slaven Bilic has however revealed that the forward will be out for another eight weeks, until mid-February.
West Ham in 2014 were fined by Fifa after Sakho withdrew from the Senegal squad with a back injury only to play and score 18 days later in West Ham's FA Cup 1-0 win at Bristol City.