The 25-year-old Dutchman underwent ankle surgery last week.
“It’s going to be very difficult for him to play this season,” said Swans boss Brendan Rodgers.
“When he was opened up and they dug deeper, they noticed some problems on the other side of his ankle.
“We are looking at eight weeks minimum, which, if it’s that, it would make it difficult for him to come back before the end of the season.”
Agustien’s current contract with Swansea is set to expire at the end of the season.
“As far as his contract goes, he doesn’t have to worry about that,” Rodgers continued.
“He is a player who has contributed well this season.
“Maybe he hasn’t played as much as he would have wanted, but he is certainly going to be an important player for us going forward.”
