The woman is the seventh person in NSW to be diagnosed with measles, and the second in 2020 alone.
According to the health alert, she took a Virgin Australia flight to and from Ayers Rock on January 27 and travelled on a Blue Emu bus.
The previous day she visited shops and a pub in Sydney's Rose Bay - including Coles, North Cellars and The Golden Sheaf.
On January 28, she went to the 7-Day Medical Centre in Bondi Junction and Coles Eastgate shopping centre.
The following day, she went to Bondi Doctors on O'Brien St before stopping in at the Chemist Warehouse in Rose Bay.
South Eastern Sydney Deputy Director of Public Health, Dr Vicky Sheppeard, said the locations no longer posed a risk of infection but urged anyone who may need a preventative measles jab to speak to their doctor.
She said: 'Symptoms to watch out for include fever, sore eyes and a cough followed three or four days later by a red, blotchy rash that spreads from the head to the rest of the body.
'Anyone who develops symptoms of measles should phone their GP to ensure they don’t wait alongside other patients before seeing their doctor.'
The warning is particularly important for pregnant women, young children or the elderly with vulnerable immune systems.
The virus is highly contagious for anyone who hasn't been immunised against measles.
While it has been eradicated from Australia, measles remains a problem in other countries and travellers may be unaware they are infected.
Dr Sheppeard said: 'It’s free for anyone born during or after 1966 who hasn’t already had two doses. If you’re unsure whether you’ve had two doses, it’s safe to have another.'