The 26-year-old South Korean did not play in the Swans’ final home Premier League game of the season on Sunday against Manchester City, having had a minor operation.
And Monk admits he had been managing the problem since last summer but could not afford to take any more risks with his midfielder.
The Swansea manager said: “All players carry niggles and you have to decide whether you can manage it or it needs to be dealt with immediately.
“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 on loan 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.”
Sung-Yueng had fallen out of favour under previous Swansea boss Michael Laudrup but when Monk replaced the Dane he handed the player a new four-year contract which ties him to the Liberty Stadium until 2018.
Ki has since enjoyed the most productive spell of his career, making 33 league appearances during 2014/15 and scoring eight goals.
He underwent surgery to allow him to return in time for Swansea’s pre-season preparation.