Bradley fell awkwardly near the touchline in stoppage time in an incident that sparked a melee when Arsenal's Gabriel Martinelli pushed him off the pitch, thinking the Liverpool player was attempting to run down the clock.
Bradley was eventually taken off on a stretcher, and Martinelli later apologised for his reaction in the heat of the moment.
"Liverpool FC can confirm Conor Bradley has sustained a significant knee injury," the club said in a statement.
"Bradley will undergo surgery in the coming days and then begin a period of rehabilitation at the AXA Training Centre. No timeframe is being placed on his return to playing at this stage of the process."
It has been reported that it was a season-ending injury, although Bradley had not ruptured his anterior cruciate ligament. However, he did suffer damage to the bone and ligaments in his left knee.
It is another blow to the 22-year-old who has missed more than 50 games in his fledgling career because of injuries in the last three seasons.
Liverpool next host Barnsley in the third round of the FA Cup on Monday.