Manager Steve Bruce confirmed after last weekend's 1-0 Premier League defeat at Stoke City that the Republic of Ireland international would miss a significant period of time.
Brady subsequently underwent a scan, which revealed damage to his right calf.
"Robbie Brady faces a spell on the sidelines after an MRI scan revealed the Republic of Ireland international suffered a significant muscle injury to his right calf in training last week," read a statement on Hull's official website.
"The club's medical staff have estimated that the injury will take 5-6 weeks to heal."
Brady, who has made 24 appearances for Hull this season, becomes the latest member of Bruce's squad to have sustained an injury this term.
The club welcome fellow strugglers Sunderland to the KC Stadium on Tuesday, with the likes of Liam Rosenior (hamstring), Mohamed Diame (knee), James Chester (shoulder) and Robert Snodgrass (knee) all absent.
