The 25-year-old suffered the injury when he fell awkwardly during the Clarets' 1-0 defeat at Leicester City on Saturday, with subsequent media reports suggesting that he could now be out for the rest of the season.
The Republic of Ireland international has since been under medical assessment by club doctors, who have confirmed a tear to his patellar tendon.
"Robbie will have surgery to repair a patellar tendon tear and will be out for a substantial recovery period," manager Sean Dyche told the Burnley website.
"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."
Prior to his injury Brady had been an ever-present for Burnley in the Premier League, helping them up to an impressive seventh place in the table.