All players arriving in Australia for the competition must undergo a two-week quarantine period, but are usually allowed to leave their hotel rooms to practice outside for several hours per day.
However, those players on the affected flight from Los Angeles to Melbourne have been deemed close contacts and will not be allowed out to train.
Victoria's Department of Health and Human Services said in a statement on Saturday a crew member and an Australian Open participant who is not a player have been taken to a health hotel after returning positive tests.
"All remaining 66 passengers on the flight have been determined to be close contacts," the statement said.
"Any players and support people will not be able to leave quarantine to attend training.
"Upon arrival to Australia all players are immediately placed in a secure quarantine environment for 14 days under the authority of Covid Quarantine Victoria and will undergo a more rigorous testing schedule than for most returning travellers."
Tournament organisers spent several months negotiating an arrangement that was acceptable to local and national government agencies regarding the admission of more than 1,000 tennis players and associated personnel to Australia.
The Australian Open begins on February 8 in Melbourne.
Additional reporting by PA.