The Scotland winger, 26, suffered the injury in Saturday's 1-0 win at QPR.
Bruce said Snodgrass, who joined Hull in a £6m deal from relegated Norwich this summer, would be missing "for the best part of the season".
Snodgrass was due to see a specialist on Wednesday to undergo surgery.
The player tweeted: "Gutted ....!!! But I will work as hard as I can to come back fitter and stronger."
"We've lost Robert Snodgrass and the diagnosis is he'll be gone for six months which is a big blow to us," Bruce told reporters at Humberside Airport before flying to Belgium for Thursday's Europa League tie with Lokeren
"We spent a lot of money adding to our midfield area and now we've lost Snodgrass for the best part of the season. It's a tragedy for him and for us.
"It's a huge blow. He was brought in to bring that little bit of quality to the midfield area."
Bruce added that he would seek to sign a replacement for Snodgrass before the end of the transfer window.
Snodgrass scored seven goals in 34 appearances last season as the Canaries were relegated from the Premier League.
The player will also miss Scotland's four opening European Championship qualifiers, as well as a friendly against England in November.
"Robert has given everything to become the influential player he has," said Scotland manager Gordon Strachan. "He is a popular guy around the squad, has a first-class attitude and a work-rate that has taken him to the level he has attained.
"It's a shame that this terrible injury has occurred at the start of a new season, with a new club and a new qualifying campaign to look forward to but the best players overcome such adversity in the long run and I have no doubts Robert will do just that."
Hull midfielder Robert Snodgrass will be out for up to six months with a dislocated kneecap, manager Steve Bruce has confirmed.