The 40-year-old had an operation this week on his anterior cruciate ligament and could be out for up to eight months.
The 30-year-old rejoined City in 2020 after a spell with Lyon, having previously played for them from 2014 to 2017.
The Giants face Wigan in the final at the Tottenham Hotspur Stadium on Saturday after Watson oversaw a major reshuffle this season.