The Scotland midfielder - bought from Norwich in June - was injured during his new club's 1-0 win at QPR on the opening day of the Premier League season.
Snodgrass has since visited a specialist and been told he will need surgery to repair damaged knee ligaments.
And speaking ahead of his side's trip to Belgium for Thursday's Europa League tie at Lokeren, manager Steve Bruce told Sky Sports News HQ he is now in the market for a replacement before the transfer deadline.
He said: "We've lost Robert Snodgrass now and with the diagnosis we think we're going to lose him for six months, which is a big blow to us all because we've spent a hell of a lot of money on that midfield area.
"We've lost him for the best part of the season. It's a tragedy for him and for us so we will have to be in the market, definitely."
Snodgrass later tweeted: "Gutted ....!!! But I will work as hard as I can to come back fitter and stronger."