The staff member is now in quarantine in Queensland and is awaiting final confirmation of their negative status, which is expected later today.
In a statement, the Australian Olympic Committee said the impact on the rest of the athletics team training in Cairns has been "minimal" and that athletes will be taking part in an organised track meet scheduled for today.
"The team will continue to be tested during its training camp in Cairns and will complete the mandatory 96 hour and 72 hours tests prior to departure for Tokyo," the AOC said in a statement.
"We are very pleased proper processes have been followed at every step by Athletics Australia, who will continue to liaise with the Queensland Health authorities."
Two days ago, tennis star Alex de Minaur had to pull out of the Games after testing positive to coronavirus.
Meanwhile the Australian Olympic Committee announced on Sunday its biggest influx of the Tokyo Games had arrived, including 340 athletes, staff and officials.
There are now 243 Australian athletes on the ground in Japan and 194 in the village. A further 49 athletes are being housed in out-of-village accommodation or training camps.
Australian team chef de mission Ian Chesterman said in Tokyo said the experience had been positive so far.
"We have been very conscious that while these Games are different, the experience in our allotment had to be positive," he said in a statement.
"Each team receives a full briefing on arrival, including details of our COVID counter-measures that are particular to our space, on top of the playbook protocols."
More infections reported in Tokyo Olympics athletes' village
Tokyo Olympics organisers on Sunday reported three new cases of COVID-19 infection among athletes, up from one new case a day earlier, as the population of the athletes' village swells ahead of the start of the pandemic-hit Games next week.
Organisers reported 10 new cases connected to the Olympics including media, contractors and other personnel, down from 15 on Saturday.
An International Olympic Committee member from South Korea tested positive for the coronavirus on landing in Tokyo. Ryu Seung-min, a former Olympic athlete, is vaccinated, reflecting the infection risk even from vaccinated attendees.
The latest cases are a blow to the local organisers and the International Olympic Committee, who have insisted the Games will not become a super-spreader event.
The cases at the athletes' village, a 44-hectare site built on Tokyo's waterfront, is particularly worrying as the majority of the 11,000 competitors will be staying there.
IOC President Thomas Bach, facing unprecedented opposition to an Olympics days before it starts, acknowledged the concerns in the Japanese public but urged them to welcome the athletes.
Mr Bach said he was hoping domestic sporting success could help shift the mood from what he said bordered on the aggressive to something more supportive.
"We are well aware of the scepticism a number of people have here in Japan. We ask and invite the Japanese people, humbly, to welcome and support the athletes from around the world," Mr Bach told a news conference.
"We are also confident once the Japanese people will see the Japanese athletes successfully performing in the Olympic Games then the attitude may become less emotional."
Originally intended to showcase Japan's recovery from its 2011 earthquake and nuclear disaster, the Tokyo Olympics has become an exercise in damage limitation.
Postponed for a year due to the global pandemic, it is being held mostly without spectators and under tight quarantine rules. Most athletes are starting to arrive for the Games, which run from 23 July to 8 August.
The Japanese public has been wary about hosting the Games at all amid a resurgence in new coronavirus infections and worries that an influx of visitors may create a super-spreader event, straining an already-stretched medical system.
Only around 20 per cent of the population is fully vaccinated.
Although Japan has escaped the explosive outbreaks of other nations, it has recorded more than 820,000 cases and about 15,000 deaths. The number of new cases in host city Tokyo, which is in its fourth state of emergency over the virus, has been over 1,000 for four straight days.
Tokyo 2020 President Seiko Hashimoto also acknowledged the public's concerns.
"I understand that there are still many worrying factors. Organisers must try to make sure that people understand that these games are safe and secure," she told a news conference on Saturday.
So far, more than 40 people involved in the Games, including Japanese and foreigners, have tested positive for the virus.
Toshiro Muto, chief of the Tokyo 2020 organising committee, said on Saturday officials were working on the assumption that there would be positive COVID-19 cases.
A key part of the anti-contagion measures is daily saliva testing of the athletes who take part, as well as frequent testing of others involved in the event. Visitors' movements are also due to be monitored and restricted.
But in a sign that the organisers were already finding rules difficult to enforce, Ugandan weightlifter Julius Ssekitoleko went missing from his team's training site in Osaka on Friday.
Authorities are still looking for him, according to Games organisers. Media reports said he left behind a note saying he wanted to stay and work in Japan, as life in Uganda was difficult.
Additional reporting: Reuters