The Summer Games are scheduled to begin on 23 July, after being delayed by 12 months because of the Covid-19 pandemic.
The International Olympic Committee said vaccination is "encouraged" but not compulsory for athletes.
Guam, Marshall Islands, Federated States of Micronesia, Palau, American Samoa, Australia and New Zealand have begun vaccination programs in recent months.
Oceania National Olympic Committees (ONOC) President, Dr Robin Mitchell, said if athletes had the option of receiving the vaccine they should take it.