The 19 nurses were due to fly out of Port Vila on Wednesday on an Air Vanuatu charter flight but were told they couldn't board the plane.
One of them, Dudley Toata, said they were told they could not return if they were not fully vaccinated against covid-19.
However, he says they weren't told this before they went to the airport.
Due to two detected positive covid cases in Port Vila among passengers from New Caledonia, the Solomon Islands government has declared that everyone coming into the country must be fully vaccinated.