Tigers manager Steve Bruce told local media that the former Norwich winger suffered a dislocated kneecap and damaged ligaments in the opening match of the season against QPR.
Bruce added that Snodgrass will see a specialist on Wednesday, but BBC Radio Humberside's David Burns said that Bruce is expecting to be without one of his biggest summer signings for almost the entire season.
Scotland international Snodgrass only joined Hull in June, being sold by relegated Norwich for a reported £6 million.
His injury came just before half-time in the opening match of the season, with the player immediately being subbed off.
- Sports & Recreation
- BBC Radio Humberside