Chelsea say she will be assessed by a specialist in the coming days and then begin her rehabilitation.
The 30-year-old Australia captain has scored 99 goals in 128 matches since signing for Chelsea in 2019.
The Blues lead the Women’s Super League by three points from Manchester City.
During her time at Chelsea, Kerr has won four WSL titles, three FA Cups, two Women’s League Cups and the Women’s Community Shield.
She has also won the Golden Boot twice, and was runner-up to Spain’s Aitana Bonmati at the Ballon d’Or awards last year.
This season, she has scored four goals in eight WSL games for the Blues and has excelled in the Champions League, scoring five goals in four matches.
The Blues said: “Everyone at Chelsea would like to wish Sam the very best for her recovery.”
Kerr, who missed part of last summer’s World Cup with a calf injury sustained in training, had just recovered from a foot injury which kept her out of her country’s friendly internationals against Canada last month.
As well as the remainder of Chelsea’s season, she will also miss Australia’s Olympic qualifiers against Uzbekistan next month and would also be out of this summer’s Paris Games, if they qualify.
“Considering how hard Sam has worked over the past six months to return to play, this news is a devastating blow for everyone,” said Australia coach Tony Gustavsson.
“With her ability to lead by example, Sam’s guidance and influence on the team is significant and, as a result, this will be an incredible loss for the national team.
“Our focus now is on ensuring she has all the support she wants and needs to navigate recovery and rehab.”
She joins a long list of women’s players who have suffered similar injuries with England duo Beth Mead and Leah Williamson, Vivianne Miedema of the Netherlands and Canada’s Janine Beckie all missing the World Cup.
Writing on X, formerly known as Twitter, Mead wrote: “Gutted for you, no words will help right now but sending big love and wishing you a speedy recovery.”
Former England and Chelsea defender Gilly Flaherty told BBC Sport Kerr’s injury would be a “huge blow” for the Blues.
“An ACL injury isn’t one that you can be back from in six to eight weeks. You know her season is done and you might not see her again until the end of the year if all goes well,” she said.
“The first thing I thought of wasn’t anything to do with Chelsea missing her, but her contract runs out at the end of the season, so I just wonder what happens next.”
Flaherty added: “She had a really tough season last year physically because Fran Kirby and Pernille Harder were out for a lot of it. Kerr had to carry a lot for Chelsea. She was really their only main striker.
“She can be quiet for 80 minutes in a game, http://tampansamping.com/ then Guro Reiten puts a ball into the box and you know Sam Kerr is a banker. If it’s a header or she’s in the right area, she will put it away. She leads the line for Chelsea and has the experience. She had such a big 12 months but got injured going into the Olympics and then at the World Cup. Chelsea have tried to manage her minutes and it’s just unfortunate timing straight after the Christmas break.”