Jabeur, 30, has dropped down to 39th in the world rankings after injury problems last year prevented her from competing at the US Open and Paris Olympics.
She ended her 2024 season in September, returning to action at the beginning of this year and suggested the long spell away had caused her asthma problems to resurface.
“Having taken off a lot [of time] didn’t help. I think it provoked it even more,” she said.
“I think I will have to find a way to feel better the next two days, which I am hoping to do because this started kind of two days or three days ago. I feel like it got worse for some reason.”
Jabeur will face American eighth seed Emma Navarro, who beat China’s Wang Xiyu 6-3 3-6 6-4, in the next round.
“I’m really just taking it one minute at a time and see how it’s going to go, but definitely I’m doing everything that I can to be ready,” said Jabeur.
“I don’t want to be greedy just after coming back from an injury. Sometimes I get angry because I feel like I’m getting back there, but every time something happens.”
Meanwhile, 2022 Wimbledon champion Elena Rybakina beat 17-year-old American wildcard Iva Jovic 6-0 6-3 to seal her 50th Grand Slam match win.
Jovic was the youngest woman in the second round of the draw but struggled against 2023 Australian Open finalist Rybakina, who is ranked 184 places above Jovic.
The Kazakh will face Ukrainian 32nd seed Dayana Yastremska, who reached the semi-finals last year as a qualifier, in the third round.
Former Australian Open finalist Danielle Collins overcame a second-set scare to beat Australian qualifier Destanee Aiava 7-6 (4) 4-6 6-2.
The American 10th seed was booed off court by the raucous Melbourne crowd as she blew them kisses and cupped her ears.
Collins, 31, will face compatriot Madison Keys, who beat Romania’s Gabriela Ruse 7-6 (7-1) 2-6 7-5, in the next round.
German lucky loser Eva Lys booked her place in the third round after beating France’s Varvara Gracheva 6-2 3-6 6-4.
The 23-year-old, ranked 128 in the world, thought she was going home after losing in the qualifying phase last week but was called up when 13th seed Anna Kalinskaya withdrew in the first round and has now won both of her matches in Melbourne.
Ukrainian 28th seed Elina Svitolina cruised past American Caroline Dolehide 6-1 6-4 and could face Italian fourth seed Jasmine Paolini in the next round.