Burnley and Republic of Ireland forward midfielder faces a "substantial" absence and knee surgery following the injury sustained at Leicester last Saturday.
Brady has made 31 appearances for the Clarets since his then club record signing from Norwich, for a fee reportedly rising to £13million. No time frame was placed on his rehabilitation.
Burnley boss Sean Dyche said on the club's official website: "Robbie will have surgery to repair a patellar tendon tear and will be out for a substantial recovery period.
"He will be given all the time and care he needs on his recovery and supported throughout from all of us at Burnley Football Club."
The 25-year-old scored his first goal of the season at Bournemouth, helping Burnley to a fourth away win and their best start to a top-flight season since 1973-74.
The Clarets are seventh ahead of Saturday's match at home to Watford.