"These restrictions have been applied in the interest of the ongoing health and safety of our residents,"the Palm Island Aboriginal Shire Council said in a statement on Tuesday.
On Cape York,the Northern Peninsula Area Regional Council has also restricted both in- and outbound travel to the region to that which is"essential"and"urgent".
Lockhart River,also on the peninsula,was expected to introduce similar measures on Wednesday.
Australia's chief medical officer Brendan Murphy has flagged particular concerns for those in Indigenous communities.
Prime Minister Scott Morrison said on Wednesday it was important to limit visitation to such sensitive areas,with a list being drawn up in consultation with the states and territories.
Those who travel from remote communities to Cairns for health appointments,and may come into contact with tourists,were also of concern to Premier Annastacia Palaszczuk.