Lee was carried off the field in Saturday’s 1-0 over Oman after a tackle by Abdul Salam Al Mukhaini in the 78th minute.
The South Korean midfielder’s injury appears to be worse than at first thought and he could now be on the sidelines for three weeks.
"Yes, he has a fracture in his right leg," a spokesman for the KFA told PERFORM.
"But it's not serious, it's a hairline fracture."
The spokesman would not confirm how long the player would be out of action but did say that he would miss the match against Kuwait on Tuesday.