The mother contracted Zika in Haiti and came to Florida to deliver the baby, said a statement from Governor Rick Scott's office.
The Florida Department of Health confirmed the case.
Zika is primarily transmitted by mosquitoes but can also be spread by sexual contact.
"It is heartbreaking to learn that a baby has been born with Zika-related microcephaly in our state and my thoughts and prayers are with the mother and child," Scott said in a statement.
"The Olympics will begin in less than 40 days and millions of Americans will travel through our state to and from Brazil, a country where the Zika virus is rapidly spreading, and we must be prepared," said Scott.
Zika can cause microcephaly, an irreversible condition in which babies are born with unusually small heads and deformed brains.
Four infants have been born with birth defects related to the Zika virus in the United States, including in Hawaii and New Jersey, according to the US Centers for Disease Control and Prevention.
There have been four US pregnancy losses involving Zika, and one in the US territory of Puerto Rico, the agency said, without offering details on whether the cases involved miscarriage or abortion.
So far this year, Florida has reported 223 cases of Zika infection, including 40 involving pregnant women.
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