The abandoned match comes the day after their second match was also deserted due to rainfall.
Australia now lead the multi-format series 4- after winning the first T20 by nine wickets.
Victory for Australia in the Test will mean they will retain the Ashes as England would only be able to earn an 8-8 draw at best.
Since the first multi-format series in 2013, three of the five Tests have been drawn.
The Test will reward four points to the winner.
England are looking to redeem themselves in Australia after they were thrashed 12-4 in the last Ashes three years ago.
When is the Australia v England Test?
The one-off Test match begins on Thursday January 26 and will conclude on Sunday January 30.
The four-day Test at the Manuka Oval starts at 11pm GMT.
How to watch on TV
BT will also be offering highlights for the Women’s series across their channel.
BBC Sport also provide short highlights after each match throughout the series.
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