Cricket Australia (CA) has announced the one-off Test against Afghanistan and the ODI series against New Zealand have been postponed due to the ongoing impact of the coronavirus pandemic.
Australia were due to face Afghanistan in the longest format for the first time in Perth in November, but that one-off game will not go ahead as planned.
The rescheduled IPL season - which is due to finish in early November - created issues over Australian players quarantining upon their return from the Twenty20 tournament in the United Arab Emirates.
New Zealand's limited-overs tour in January 2021 has also been called off amid "the challenges around international travel and quarantine restrictions" caused by the global health pandemic.
CA hopes to find new dates for the fixtures in the coming years, with the postponements meaning India will be the only international side to visit Australia during the 2020-21 season.
"Cricket Australia looks forward to working with our good friends at the Afghanistan Cricket Board and New Zealand Cricket to deliver the matches at a time when, hopefully, the restrictions brought on by the COVID-19 pandemic have eased," CA's interim CEO Nick Hockley said in a statement.
"We all worked incredibly hard to make the series happen this summer, but the challenges around international travel and quarantine restrictions ultimately convinced all parties that the series would need to be played at a later date.
"CA looks forward to welcoming the Indian men's team for a full schedule of matches this summer in what promises to be an incredible contest across all three formats.
"CA would also like to take this opportunity to thank our wonderful partners for their understanding and support as we have navigated the complexities of hosting international sport during a pandemic to deliver a thrilling summer across men's and women's cricket at international and domestic level."
Australia are due to face India in a four-Test series, as well as three one-dayers and a trio of Twenty20 fixtures. Details over the schedule are yet to be confirmed.