Agustien picked up the injury in the FA Cup third-round replay defeat at Arsenal and tried to play on before being withdrawn.
The problem is set to keep the 26-year-old out of Swansea's next five games, including the second leg of the Capital One Cup semi-final against Chelsea.
Manager Michael Laudrup said: "We had bad news after losing the other day, we have lost Kemy Agustien for, I think, the next four weeks with his ankle.
"He twisted it in the first half, he tried to start the second half and there was some problem with the ligaments.
"It could have been a lot worse, but still four weeks means he will be out for at least our next five games, four in the league and the game on Wednesday (against Chelsea) as well."
Agustien missed almost three months earlier this season after being injured in a serious car accident in his home country.
But he has featured regularly since returning to action in November, making 15 appearances in total and excelling in the 1-1 draw with Manchester United just before Christmas.
Laudrup is not short of midfield options with the likes of Leon Britton, Ki Sung-yueng and Jonathan de Guzman in his squad, but admits the injury has not come at the best time during a busy January.
He said: "It means we are a number down, missing a player who has been participating in the last month and a half and it puts extra work on the rest of the players in the midfield which I have to think about when we are playing every three of four days, so we will have to see.
"I still have plenty of possibilities and Roland Lamah has come in so he will be in the 18 tomorrow."
South Wales has been heavily hit by snow over the last 24 hours, and several members of Laudrup's squad were unable to report for training this morning due to the conditions.
But the Dane is confident Saturday's Barclays Premier League fixture against Stoke will go ahead as scheduled.
He said: "I have noticed when I have been in the UK that when it is snowing a lot of things stop, but I hope all the players will be here tomorrow and I am sure we will play the game.
"There were seven or eight players not training today but I think we can deal with that."