The centre-back sustained the injury during a training session with the England national team on Wednesday.
The issue was isolated to Gomez’s tendon, with no damage to any other associated knee ligaments.
The operation to correct the damage, which took place in London on Thursday morning, was a success and the 23-year-old will make a full recovery.
Gomez will begin a rehabilitation programme with the Reds’ medical team immediately, with club staff carefully monitoring his progress.
No timescale is being placed upon his return, though the issue is likely to rule him out for a significant part of the remainder of 2020-21.