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."

The former London Irish man, 29, who can play in the second or back row, was injured in Friday's loss at Newcastle.
"He really hurt his neck and he has got pins and needles in his arms and through his hands," director of rugby Todd Blackadder told BBC Points West.
"So he could be out for a little while yet but it's hopefully not too serious. But to lose a big boy like that is an opportunity for someone else."

Rescuers managed to return three other beached whales to the sea.
Fire crews sprayed the whales with seawater as local teams tried to return them to the sea.
Expert Jacky Karpouzopoulos, of the Centre for Marine Mammal Research at La Rochelle, said the beaching may have followed the death of a dominant male in the pod.
He told La Voix du Nord newspaper that the whales could have been one family of which the dominant male died at sea and the others followed his body to the shore.
"The group was in the middle of a deep-sea migration towards the Faroe Islands to reproduce and feed," he said.
Mr Karpouzopoulos described the beaching of so many whales as "exceptional".
About 400 local residents went to the beach to try to help the rescue operation, La Voix du Nord reported.
It said that two of the rescued whales stayed close to the shore, as if waiting for the others to be returned.
The largest of the dead whales was a male more than 5m (16ft) long.
Autopsies will be carried out at the University of Liege to determine the cause of death.
Hull midfielder Robert Snodgrass will be out for up to six months with a dislocated kneecap, manager Steve Bruce has confirmed.
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Bath forward Matt Garvey is to have surgery after sustaining a neck injury.
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Seven pilot whales have died after being found stranded on a beach at the northern French port of Calais.