The Australia international - regarded as one of the best players in the world - suffered the problem during a practice session in Morocco and will see a specialist in the coming days.
Chelsea have not put a timeframe on Kerr's recovery, nor did they specify whether Kerr had suffered a complete ACL rupture, but the 30-year-old will be expected to spend months recovering and will miss the remainder of the 2023-24 season.
"Chelsea Football Club can confirm striker Sam Kerr has sustained an anterior cruciate ligament (ACL) injury during our warm weather training camp in Morocco," Chelsea said in a statement.
"Sam will be assessed by a specialist in the coming days and then begin her rehabilitation with the club's medical team. Everyone at Chelsea would like to wish Sam the very best for her recovery."
As well as sitting out the rest of Chelsea's domestic and Champions League campaign, Kerr will be unavailable for Australia Women's Olympic qualification double-header with Uzbekistan next month, where victory will ensure the Matildas' place at the 2024 Paris Games.
Should Australia qualify for this summer's Olympics, Kerr would also be expected to miss the tournament, and head coach Tony Gustavsson labelled news of the forward's injury "devastating".
"Considering how hard Sam has worked over the past six months to return to play, this news is a devastating blow for everyone," Gustavsson told the official Matildas website.
"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."
Kerr has proven herself as a prolific goalscorer since joining Chelsea from Chicago Red Stars in 2020, scoring 99 goals in 128 matches for Emma Hayes's side, including nine goals from 12 games in the first half of the 2023-24 season.
As well as collecting 10 team honours with Chelsea, the 30-year-old won the WSL Golden Boot in the 2020-21 and 2021-22 seasons and placed second in the 2023 Ballon d'Or Feminin behind Barcelona and Spain midfielder Aitana Bonmati.
Kerr is one of a plethora of high-profile women's players to suffer ACL injuries in recent memory, a list which also includes Arsenal trio Leah Williamson, Beth Mead and Vivianne Miedema, as well as two-time Ballon d'Or winner Alexia Putellas.
Chelsea hold a three-point lead over Manchester City and Arsenal at the top of the Women's Super League table and return to action at home to West Ham United in the fourth round of the FA Cup next Sunday.