The luckless Hammers striker suffered a hamstring problem just 12 minutes into Tuesday night's 3-1 win at Bournemouth.
Bilic admits the 27-year-old is "gutted" at facing yet another spell on the sidelines.
"He's having a scan but it's another one of those, four to six weeks," said Bilic.
"He's a positive lad, but of course he is gutted for several reasons. He felt he was back and enjoying his football.
"It's not the end of the world, though. If everything goes well he will be back very soon so there is no reason to be negative.
"If it goes as we expect then he will be back for a significant part of the season, the last 10-15 games, with enough time to make a huge impact on our season."
Carroll has been hit by injuries since moving to Upton Park, making just 31 starts in three years following his club-record £18million switch from Liverpool.
He returned to action in September following a long-term ankle injury and then had a spell out before Christmas with a groin strain.
However, Carroll has scored twice in his last four appearances, helping the Hammers to victories over Southampton and Liverpool, so his latest absence is another blow especially as fellow striker Diafra Sakho is still missing with a thigh problem.
Bilic does, though, have some positive fitness news with winger Victor Moses available to face Newcastle on Saturday after six weeks out with a hamstring injury.
Midfielder Cheikhou Kouyate and forward Mauro Zarate are also fit after missing the Bournemouth game.