However she will remain under observation.
Queensland Premier Campbell Newman said the negative test result was heartening but the World Health Organisation required three full days of negative tests.
"Let's keep our fingers crossed for the patient involved," he told reporters in Canberra.
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Several New Zealanders have also been working with the Red Cross in Sierra Leone. Nurse Donna Collins, a Tutukaka mother of four, and Sharon Mackie, a Wellington health service co-ordinator, left in August for a three-week stint.
Last night, health authorities moved to reassure New Zealanders that adequate screening processes were in place for anyone arriving from affected countries.
The Director of Public Health, Dr Darren Hunt, said the health sector was well set up to manage cases of Ebola but it was unlikely someone with the disease would arrive here.
"Ebola is not easy to catch; it's not as infectious as the flu or measles. Infection requires direct contact with infected body fluids."
Anyone arriving in New Zealand who in the past month had visited West African countries affected by the Ebola outbreak was screened for symptoms or possible exposure.
"Since screening was introduced early in August, 58 people have been screened but none have caused concern."
Before she left for West Africa, Ms Kovack told the Cairns Post she was "a little bit nervous, a little bit anxious".
There have been three suspected cases of Ebola investigated in Australia: a woman in Perth who attended a conference in Africa, a 1-year-old child in Victoria, and a Gold Coast man who complained of vague symptoms while in police custody. All were cleared of having the killer virus.