The 32-year-old rose to head home a Niamh Charles cross in the 13th minute of Chelsea's 3-1 win over Leicester City at King Power stadium, moving ahead of Fran Kirby on the list of goalscorers for the eight-times WSL champions.
"I'm absolutely stoked to break ... the record, it feels amazing to be in the same category as some of those players," Kerr said in a message to fans on the club's social media.
"But I'm absolutely honoured and it's been amazing to score 64 goals in front of all of you - let's finish off the season strong."
Kerr is Australia's all time leading goalscorer with 75 in 139 internationals and she won the WSL's golden boot in the 2020-21 and 2021-22 seasons with tallies of 21 and 20 goals.