The Republic of Ireland international has been dogged by injuries this season, limiting him to just 11 starts in all competitions for Steve Bruce's side.
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"Robbie went to see a specialist who advised him to have an operation on the groin," confirmed Bruce.
"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."
Despite being without the likes of Brady and striker Sone Aluko for much of the season, Bruce's Hull sit 12th in the Premier League - six points off the relegation zone - and will contest an FA Cup quarter-final with Sunderland on Sunday.