It added that neither mother nor child is still infected and that there is no danger to anyone in Hawaii.
For the first time, a baby was born with the Zika virus in the USA this week.
"We are saddened by the events that have affected this mother and her newborn", said Sarah Park, a Hawaiian state epidemiologist. She was likely infected from a mosquito bite early in her pregnancy and the virus then damaged the developing brain of the fetus.
The United States warned pregnant women to avoid travel to 14 countries including Brazil due to the mosquito-borne Zika virus, which has been linked to birth defects. They are Brazil, Colombia, El Salvador, Guatemala, Mexico, Panama, Paraguay, Suriname, Haiti, Puerto Rico, Martinique, French Guiana, Honduras, Guyana, and Venezuela.
"This case further emphasizes the importance of the CDC travel recommendations released today", Park added. The Rio games are slated to run from August 5 to August 21.
As the number of reported Zika infections has risen, so have instances of microcephaly.
And this past week, the CDC confirmed it had found evidence of the virus in the brains of two Brazilian infants with the condition who died shortly after birth.
Women considering becoming pregnant were advised to consult doctors before going to Zika-infested areas, and all travelers headed to such areas were urged to take vigorous measures to avoid mosquito bites.
"Until more is known, and out of an abundance of caution, CDC recommends special precautions for pregnant women and women trying to become pregnant".
"In this situation, an astute Hawaii physician recognized the possible role of Zika virus infection, immediately notified the Department of Health, and worked with us to confirm the suspected diagnosis".
Anyone who has not previously had Zika and is traveling in an area where Zika is an issue could be at risk.
The first US case of a baby infected in the womb was reported Friday in Hawaii. The infected person had not travelled.
The Zika virus is spread by the Aedes aegypti mosquito, which can also carry dengue and chikungunya.
But Brazil has been raising increasingly loud alarms about Zika.
The Zika and dengue viruses - like virtually all mosquito-borne diseases - do not occur in mosquito larvae.
The ministry said people can destroy mosquito-breeding sites by looking for anything around the home, school, churches, and business places that may collect water and either cover it, keep it dry or dispose of it. fix leaking pipes and outdoor faucets, cut the grass short and trim shrubbery, clear roof gutters and eaves to prevent water from settling and fill in and drain any low places in the yard such as areas where there are usually puddles when it rains.