Kerr joined the Addicks at Under-14 level and captained Kent Schools before playing for Charlton's development squad.
Women's boss Riteesh Mishra said: "The news is tragic. My heart goes out to Lucy’s family and friends.
"She was there at the start of my journey with Charlton as a coach with the Under 16s.
"Her personality and attitude in particular were infectious and she always put a smile on the faces of staff.
"She will be in our thoughts and forever be part of our Charlton family."
Charlton Women are next in action on Sunday, when they travel to face Blackburn Rovers in the Championship. Their next home fixture comes against London Bees on March 22.
Sheppey Angels FC, another team Kerr played for, paid tribute to a "beautiful, amazing and talented young lady".
They wrote on Facebook: "As a club we never thought that we’d be writing this post about one of our much loved players.
"As most of you are aware our player Lucy Kerr has been battling Cancer over the past months, she’d gone through so much and has been so incredibly brave and strong as her team mates we couldn’t of been anymore proud of her.
"Lucy is an incredible player and her ability on the pitch was outstanding you’ll never find a player like her. She put in 110% into every match and we was lucky to have her as part of our football family."