The baby girl was delivered at 34 weeks through a caesarean operation in Melbourne on 1 August.
After years of failed IVF procedures, the new mother, whose partner is 78, conceived using an embryo sourced from an overseas donor.
She and her daughter are recovering at a private hospital in Melbourne. Neither have been publicly named.
The previous Australian record was held a woman who gave birth to her first child at 60 in 2010.
Romanian woman named Adriana Iliescue set the record for being the world’s oldest mother when she gave birth in 2005 aged 66.
An Australian reproduction specialist said “responsible” IVF clinics refused treatment to women over the age of 53, which he described as the “end of natural pregnancy”.
“That child will need looking after for 20 years, and there’s a possibility she won’t be able to do that,” Monash University professor Gab Kovacs told the Herald Sun newspaper.
“Our bodies weren’t designed to have children in our 60s.”