A young woman who recently returned from travel in south-east Asia has been diagnosed with measles and may have exposed others to the highly contagious condition while spending time in Sydney's CBD.

The woman spent time at Capitol Square and World Square, and used public transport between Town Hall and Artarmon stations, while she was unknowingly infectious between April 29 and May 6.

People who visited World Square and Capitol Square in Sydney's CBD on May 5 and 6 should look out for symptoms. Credit:John Woudstra

While those sites do not pose an ongoing risk to visitors, NSW Health's director of communicable diseases Vicky Sheppeard said people who were at those locations at those times should be alert for signs of measles until May 24.

"Symptoms to watch out for include fever, sore eyes and a cough followed three or four days later by a red, spotty rash that spreads from the head to the rest of the body," Dr Sheppeard said.