Te Marae Ora was alerted to the outbreak through its Pacific Public Health Surveillance Network (PPHSN) about a week ago.
The outbreak is thought to have resulted from recent major flooding in Tahiti.
In a statement from the Ministry of Health the bacteria causing leptospirosis does not currently exist in the Cook Islands.
The ministry said staff were working with stakeholders to ensure the disease does not enter the Cook Islands.
“Te Marae Ora with border control partners will continue to monitor international vessels and aircraft and ensure that all ports are free from the breeding and resting places for rats and mice,” the ministry said in a statement.
“Te Marae Ora advises travellers to Tahiti to always wear protective clothing, especially footwear if you must wade in flood waters or other areas that might be contaminated. But you should avoid wading in these areas, especially if you have any cuts or abrasions.”
Leptospirosis is a disease caused by a bacteria called leptospira. It is commonly spread through the urine of rats or mice to humans.
Humans become infected through direct contact with the urine of infected animals or with a urine-contaminated environment.
The bacteria enter the body through cuts or abrasions on the skin, or through the mucous membranes of the mouth, nose and eyes. Person-to-person transmission is rare.
Common signs of infection are high fever, headache, chills, muscle aches, vomiting, jaundice, red eyes, abdominal pain, diarrhoea and rash.
The Ministry of Health said the main treatment for leptospirosis was antibiotics and pain relief.
“Travelers from Tahiti who experience any of these symptoms while in Rarotonga are asked to visit the hospital and tell them about your travel and that you think you have been exposed to contaminated water.”