A statement posted on the Belgian star's website Sunday said the injury would keep her out for at least four to six weeks.
"Since the French Open starts in literally six weeks, Kim's presence in Paris is very uncertain,'' the statement said.
The statement did not give details on how the injury occurred, but said that Clijsters - winner of the last two Grand Slam tournaments - had strained ligaments in her right ankle and tore an ankle joint capsule and tendon sheath.
"The consequences are serious,'' the statement said.
It was the second setback in as many weeks for the world's second-ranked player.
Last week, Clijsters announced that she'd be sidelined for a month with shoulder and wrist injuries, forcing her out of Belgium's Fed Cup semifinal against the Czech Republic this weekend.
The US Open and Australian Open champion said she had overexerted her right shoulder and wrist during her busy spring schedule on the tour. After winning the title Down Under, she played Fed Cup and a tournament in Paris in February before traveling to the United States in March to compete in Indian Wells and Miami.
She pulled out of her fourth-round match in Indian Wells and lost in the quarterfinals in Miami.
Clijsters is a two-time runner-up at the French Open.