The 1954 painting, Sylvette - featuring model and muse Sylvette David - sold to an anonymous overseas phone bidder at the Deutscher-Menzies Galleries.
One of 40 works inspired by David, it was painted by Picasso when he was 73.
The sale broke the previous record of $3.48m AUS (£1.67m), set in 2007, for a work by Australia's Brett Whiteley.
"Sydney is the New York of the art market in the southern hemisphere," said Deutscher-Menzies Galleries spokeswoman Marie Geissler.
'Historic day'
Rodney Menzies, the director of the gallery, bought the Picasso two years ago for $4.6m (£2.2m).
"It's a historic day for Australia in the sense that a very significant international picture by the greatest artist of the 20th Century was sold at an Australian auction for a record price," Mr Menzies told Agence France Presse.
Picasso came across Sylvette David, his 17-year-old neighbour, while living in the south of France.
Her tall frame and long, blond ponytail fascinated the Spanish cubist painter, who died in 1973.
BBC
| Buying | Selling | |
| Euro | 1.8126 | 1.8213 |
| Dolar | 1.3335 | 1.3399 |
| Sterlin | 2.3440 | 2.3563 |













