Hamish Pepper, Asia-Pacific forex strategist at Barclays, said: "Admittedly there was some growth in full time jobs and perhaps that was the silver lining but at the end of the day, [it was] a higher unemployment rate than we and the market had expected," said
The Australian dollar got whacked on the news, tumbling more than half a cent to $0.9283, and lost around 0.8 percent against the euro, pound and the yen.
Read MoreHousing bubble fears resurface in Australia
The data fly in the face of other recent stronger indicators: consumer sentiment bounced back strongly through July, while housing prices showed a robust increase in June and July and business conditions have lifted in recent weeks.
"The numbers suggest that the loss of momentum in Q2 continued to be a drag on the labor market into July," said Paul Bloxham, chief economist of Australia and New Zealand at HSBC.
Australia stocks: Good times to roll on
"The slowdown in growth in Q2 followed strong GDP (gross domestic product) in Q1, but also reflects the impact of falling commodity prices, a stubbornly high AUD as well as the negative reaction to the May," he added.
The poor data is also intensifying debate whether the Reserve Bank Australia (RBA) is done cutting rates. On Tuesday, the central bank left rates unchanged at the record low of 2.5 percent for a 12th month.
The Australian economy is struggling to rebalance its economy away from its once-booming resource sector, which has been hit by a fall in demand from China.
HSBC's Bloxham doesn't see further rate cuts, but a persistently weak labor market could indicate that rates will stay lower for longer, even as major central banks around the world like the Federal Reserve are looking to hike rates.
Read MoreAustralia central bank holds rates at 2.5%
"While a weaker labor market clearly increases the likelihood that the RBA could deliver further rate cuts, we still see this as unlikely given that monetary policy is already very accommodative and the housing market is already booming," Bloxham said.
"However, a weaker labor market is likely to take further pressure off wages growth, which could put downward pressure on inflation in the medium term. While we remain of the view that the RBA are unlikely to cut rates further, the clear risk is that they may be on hold for longer than previously expected," he noted.
Focus now turns to RBA's quarterly statement due out on Friday.
"Tomorrow's [Friday's] statement of monetary policy will be looked at closely as the market seeks more clues on what to expect from the RBA. What we do know though isthat the RBA is quite content with a period of stability in rates," Stan Shamu, market strategist with IG, wrote in a note.
— By CNBC's Li Anne Wong. Follow her on Twitter @LiAnneCNBC