Ayew joined the Hammers in a £20 million deal from Swansea City earlier this summer as Bilic looks to bolster his thin options in attack.
The Ghanaian was handed a start in their opening fixture of the Premier League season against London rivals Chelsea, but lasted just half an hour before having to be taken off injured in the eventual 2-1 defeat.
Now, with a hectic schedule on the horizon which will see the Irons juggle their start to the league campaign with their crucial two-legged Europa League play-off against Astra Giurgiu, Bilic has given an update on the striker.
The Croatian boss fears that he could be without his big money signing for several weeks, but admits that the true extent of his injury will not be known until later on Wednesday.
Bilic said, via the Standard: "We will wait to get the results on Andre and hopefully it is not that bad. It will be weeks and not days unfortunately.
"We will find out in the next couple of hours."
The news will come as a big blow for West Ham supporters, who saw their team struggle with injuries and poor form in attack for much of last season.
Ayew is not the only striker to arrive at the London Stadium this summer, with young prospects Ashley Fletcher and Jonathan Calleri also joining, but his price tag and form for Swansea last term meant that many hopes were being pinned on him.