Sakho has struggled with a series of injuries throughout the campaign, restricting the striker to just four Premier League appearances.
The 27-year-old featured as a substitute in last month's defeat to Arsenal, reigniting hopes he would be fit for the run-in.
But the Senegal international has suffered a back problem and will be unable to play any part in the Hammers' final three games of the season.
Bilic told his pre-match news conference: “In the beginning of pre-season, Sakho got injured, came back in the game against Spurs away, he played a bit and in the next game we played Manchester United away.
“He did his hamstring, and was out for the operation and was out for four or five months, he came back and now he has got another problem. It’s really a problem.
“He’s not fit for tomorrow [Friday] and again it’s his back and unfortunately he is out for the season. He’s been very unlucky,” the Croatian added.
Sakho's confirmed absence for Friday's clash with Tottenham is set to give Bilic a selection headache up front.
Andy Carroll has missed the last three games with a groin problem and West Ham will make a late call on the forward's fitness prior to facing Mauricio Pochettino's side.