Financial markets had expected the rate to remain steady at 4.1 per cent in June, however, there was a 34,000 increase in people without work, according to the Australian Bureau of Statistics.
Employment rose by 2,000, up two per cent compared to the same month last year, after part-time employment grew by 40,000 and full-time employment fell by 38,000.
Until this result, the unemployment rate had sat at 4.1 per cent for three consecutive monthly readings.
The Reserve Bank will closely monitor the labour market before its next monetary policy meeting in August, NAB's head of Australian economics Gareth Spence said.
"The focus for the RBA will be ensuring the labour market remains healthy going forward," he said.
"The timing of (rate) cuts is not super important.Â
"It's more about where do they end up."
In a move that shocked analysts and disappointed mortgage holders, the RBA in July kept the cash rate steady at 3.85 per cent.
Most economists had pencilled in a 25 basis point cut on the back of slowing inflation growth.
Mr Spence still expected the jobless rate to climb to 4.4 per cent by the end of 2025, but said economic indicators point to the labour market still being in a strong position.
The Reserve Bank said in its latest monetary policy decision that labour market conditions remained tight.
"Measures of labour under-utilisation are at relatively low rates and business surveys and liaison suggest that availability of labour is still a constraint for a range of employers," the bank said.
"Alternatively, labour market outcomes may prove stronger than expected, given the signal from a range of leading indicators."
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