The shelter was designed by New Zealand architectural firm Fahrensohn Architects, and will include the construction of a two-storey masonry shelter, two water tanks, and modifications of an existing septic tank system.
It is believed the building will be able to house up to 80 people and will include kitchen and toilet facilities.
The building will also be pivotal in post-disaster recovery efforts on Palmerston.
The atoll lies some 367 kilometres northwest of Aitutaki and has an estimated resident population of around 60 people.
The last cyclone to strike Palmerston was Tropical Cyclone Victor in 2016. By most accounts, it was a mild one. However, Victor still managed to reach gusts of up to 102 kilometres an hour.
Tenders for the cyclone shelter project close on June 29.