Games due to take place in England in October and November.
England's Gareth Widdop is tackled by Matt Gillett of Australia during the 2017 Rugby League World Cup final
England's three-match Ashes series with Australia has been cancelled due to the coronavirus pandemic.
The games had been due to take place in England in October and November, with the competition being revived after a 17-year absence.
Both the Rugby Football League (RFL) and its Australian counterparts will focus on completing their domestic club competitions - although talks have already begun about a series in 2022.
On the announcement, RFL chief executive Ralph Rimmer said: "We make this announcement with great reluctance and disappointment, as we had been looking forward so much to welcoming the Kangaroos for the revival of the Ashes in 2020 - and the prospect of the series had captured the imagination of our players, broadcast and commercial partners, supporters and media alike.
"However the current circumstances have had a seismic impact on rugby league, as on all other sports, and we all now need to give in order to find solutions for the greater and longer term good of the game.
Ralph Rimmer has been trying to find a solution to save the Ashes series since the outbreak
"After regular discussions with the ARLC over the last few months, combined with those within our domestic competitions, we have concluded the right thing to do for the game as a whole is to make this decision now.
"It will have a considerable impact on the finances of rugby league here in England, as we were banking on a significant boost from Australia's first full tour since 2003."
The news comes after the government provided a £16m emergency loan to the RFL at the start of May to be split amongst clubs, who can apply for a slice of the cash to sustain them.
No Super League games have been played since March 15 due to the pandemic with clubs yet to finalise plans to restart the 2020 season.
However, it could return in the middle of August with the league also setting a target of playing in front of fans again as soon as October.
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