Slovenia's Dalila Jakupovic dropped to her knees during the second set of her match against Stefanie Vogele and eventually had to be helped off the court at Melbourne Park.
"It was really bad. I never experienced something like this," Jakupovic said.
"I was really scared I would collapse because I couldn't walk any more."
Former Wimbledon finalist Eugenie Bouchard required a long medical timeout during her meeting with Xiaodi You after complaining of a sore chest, eventually returning to win in three sets.
Australia's Bernard Tomic also struggled with breathing difficulties during his loss to the seventh-seeded Denis Kudla.
Qualifying had earlier been delayed and practice temporarily suspended due to the poor air quality in Melbourne, state capital of Victoria.
"Further decisions will be made based on onsite data, and in close consultation with our medical team, the Bureau of Meteorology and scientists from EPA Victoria," officials said after that initial delay.
"As always the health and safety of our players, our staff and our fans is our priority."
Australia's wildfires have been burning since September, killing 27 people, destroying more than 2,000 homes and leading to thousands being evacuated.
Australian Open organisers have previously insisted that the first Grand Slam tournament of the year will not be delayed, with the main draw due to begin on January 20.
Conditions also affected the nearby Kooyong Classic, a warm-up exhibition for the Australian Open, where officials called a premature halt to Maria Sharapova's match against Laura Siegemund in the second set.