Snodgrass, 26, dislocated his kneecap and damaged ligaments in the opening day victory over Queens Park Rangers, his first Premier League match for Hull since joining from Norwich City for a reported seven million pounds.
"Gutted ....!!! But I will work as hard as I can to come back fitter and stronger," Snodgrass said on Twitter.
Speaking before the team flew to Belgium for their Europa League playoff match with Lokeren, manager Steve Bruce said he would miss most of the season.
"We've lost Robert Snodgrass and the diagnosis is he'll be gone for six months which is a big blow to us," he told the Hull Daily Mail.
"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."
The injury further weakens Hull's attacking options, having sold Ireland striker Shane Long to Southampton last week.
(Reporting by Josh Reich; Editing by Ossian Shine)
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