The South Korean has enjoyed a new lease of life under Monk this season, making 33 league appearances and scoring a career-high eight goals having been sent out on loan to Sunderland by former boss Michael Laudrup.
Monk revealed that the 26-year-old was carrying the knee injury on his return from the Stadium of Light, but refused to undergo treatment last summer due to the World Cup.
However, Swansea have been forced to keep a particularly close eye on the problem in recent weeks, including sending Ki in for minor surgery.
"All players carry niggles and you have to decide whether you can manage it or it needs to be dealt with immediately," Monk is quoted as saying by PA.
"Ki has been fantastic and you want someone who has done that well to be part of it to the end of the season, but you do not want to take any risks. He came back from Sunderland last summer with a sore knee and we were advised he could have the operation then, but he had the World Cup coming up.
"Understandably he did not want to miss that so he went, and since then his knee has been fine. But it had flared up a bit in recent weeks. We have had to manage it and give him a rest but he has still contributed really well."
Swansea, who have already amassed a record points haul and secured an eighth-place finish in the Premier League this season, end their campaign away to Crystal Palace on Sunday.