The 22-year-old Republic of Ireland international, who has scored four goals in 18 appearances for the Tigers this term, has been troubled by a groin problem for much of the campaign and he had an operation earlier this week.
Hull manager Steve Bruce told his club's official website: "Robbie went to see a specialist who advised him to have an operation on the groin.
"The problem has been hovering for a long time as we know, but hopefully it has been put to bed now.
"He's had the operation and is now in recovery mode. The sad thing for Robbie and for us is that I don't think he's going to have a part to play this season and he's got a long summer ahead of him.
"The operation he's had is a serious one and we wish him the best of luck. We hope that we'll see him at the start of next season."
Defender Paul McShane has also undergone surgery after he damaged ankle ligaments in the 1-0 defeat to Southampton at the KC Stadium last month - Brady also made his last appearance as a substitute in that game.
Bruce added: "It's the same for Macca in that he's got a long summer ahead and there's nothing worse than a really bad injury.
"Again we wish him well with his rehab which is going to be long and difficult, but hopefully we'll also see him back by the start of next season."