The Slovenian, 28, had to be helped off court after suffering a coughing fit in her first-round match in Melbourne.
Wednesday’s qualifying was delayed because of the “very poor” air quality from the ongoing bushfire crisis.
“It was very dangerous to play in those conditions yesterday,” said Jakupovic.
Canadian Eugenie Bouchard had to leave court to receive treatment after complaining of a sore chest during Tuesday’s first round.
Australia’s Bernard Tomic also had treatment on court and Maria Sharapova of Russia’s exhibition match in Kooyong in the east of the city was called off.
Wednesday’s qualifying resumed after a three-hour delay but heavy rain meant matches were ultimately suspended for the day.
“I think all of the players yesterday suffered more than the ones playing today because not all matches are going to be finished today,” Jakupovic told BBC Radio 5 Live Breakfast.
“Yesterday, whoever we talk to, all the players had headaches, were feeling chest pains, had problems breathing. It was horrible.”
At least 28 people have died and an estimated 10 million hectares (100,000 sq km) of land in Australia has burned since 1 July.
People in Melbourne were advised to stay indoors on Tuesday, while spectators at Melbourne Park wore breathing masks.
Jakupovic said she did not have asthma and had not had breathing problems before.
“I actually prefer the heat when I play in these conditions, so this was something very different,” she added.
“I’ve never experienced something like this.”
Britain’s Harriet Dart, who won her first-round qualifying match later on Tuesday, described playing as “a little bit different”.
“I didn’t go outside too much until my match. I think I was quite lucky to be playing later, as the conditions definitely improved as the day went on,” she said.
Dart’s second-round opponent, American Nicole Gibbs, voiced her concerns about the air quality on Wednesday.