All three had travelled to areas outside the United States where the mosquito-borne ailment is spreading rapidly, the New York State Department of Health said, without specifying where.
Officials said one person has completely recovered, while the others are still getting better.
US health authorities earlier on Friday expanded a travel warning for pregnant women to avoid 22 places in Latin America and the Caribbean due to the Zika virus.
It has been linked to thousands of cases of a birth defect known as microcephaly, when babies are born with abnormally small heads, which can cause brain damage.
New York authorities warned anyone contemplating travel to warmer regions to take care.
“We are urging residents, especially pregnant women, to check all health advisories before travelling and take preventive measures when travelling to affected countries,” said New York State Health Commissioner Howard Zucker.
Women in these areas are urged to take measures to avoid mosquito bites, including wearing long sleeves and pants, and applying insect repellent.