Turnbull's conservative government remained neck and neck with the centre-left Labor Party in the Ipsos poll, which showed the government leading with 51% support to Labor's 49%.
However, Turnbull's personal popularity as preferred prime minister fell four percentage points to 47%, which is still above opposition leader Bill Shorten at 30%.
Australians will vote on July 2 after an unusually long 74-day campaign.
Turnbull, considered a moderate in the conservative Liberal Party-led coalition government, had enjoyed high levels of popularity since he deposed his right-wing predecessor, Tony Abbott, in an internal party coup in September.
"Turnbull was expecting to run rings around Labor in this campaign and instead Labor have him in their sites," said Peter Chen, a political scientist at Sydney University.
"He would be a very nervous man this morning."
The election comes as Australia is trying to rebalance its economy away from a once-in-a-generation mining boom.
The economy, which remained relatively unscathed by the global financial crisis, has started to show signs of a slowdown in recent years.
Economic issues such as tax and the funding of education and health care have been front and centre in the campaign, as well as the hot-button issue of asylum seekers and border protection.
Australia has seen a revolving door of political leadership in recent years. If Turnbull loses on July 2, the change in prime minister would be the fifth since 2010.