Matches were pushed back by an hour and play had been underway for a few hours before conditions again deteriorated, creating difficulties for some players.
During her match against Swiss player Stefanie Vogele, 28-year-old Jakupovic was forced to abandon the game after she fell to her knees due to an apparent coughing fit. The points were getting bigger, and I couldn't breathe out on the court.
"I was surprised, I thought we would not be playing today but we don't have much choice".
Bushfire smoke has affected a number of elite sporting competitions involving soccer, rugby league and cricket, and the pollution has raised fears for player safety at Melbourne Park, with the tournament starting on Monday.
Health authorities expect the air quality to be in the "very poor to hazardous range" until at least Wednesday night.
Polluted air caused by the bushfires raging across the country meant practice sessions were halted on Tuesday ahead of next week's Australian Open, the first Grand Slam in the tennis calendar.
"We're not going to put them in harm's way or make any decision that's going to negatively impact their health and wellbeing".
Thick smoke stretched from fire-ravaged Gippsland, past Melbourne to Geelong, with "hazardous" air quality recorded across most of the state on Tuesday. "When I was on the ground it was easier to get some air".
The qualifying matches were delayed but did eventually take place, and the smoke wreaked havoc with some players' respiratory systems.
"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", a statement from organisers said.
At the Kooyong Classic exhibition event, also held in Melbourne, Russia's former No. 1 Maria Sharapova also struggled in the heat and smoke before her match was called off in the second set.