UBS expects online penetration to rise to 14 per cent by 2023, broadly in line with the global average, but 27 per cent will be driven by Amazon alone.
UBS warns discretionary retailers will need to improve price, range and service as margins are squeezed.
"Online take-up will be driven by consumers' ability to get what they want [range], when they need it [delivery] at a good price," said UBS retail analyst Ben Gilbert.
"As range and scale builds we expect share gains to accelerate (per offshore experience) and remain comfortable with our A$4 billion ($4.2b) revenue target for Amazon in Australia by FY23."
The UBS report favours companies with limited exposure to the dominance of Amazon, including Woolworths, grocery supplier Metcash and Penfolds Wine distributor Treasury Wine Estates.
But it expects margins to be squeezed at a number of clothing and electrical goods retailers.
UBS conducted a survey of 1002 Australian consumers and found 93 per cent of consumers are aware of Amazon, 56 per cent have visited Amazon.com.au, 22 per cent have purchased and 29 per cent see a high likelihood of it becoming their main online shopping destination.