And in Puerto Rico, where screening has been recommended since February, almost 1% of blood samples from donors with no symptoms of Zika turned up positive for the virus, according to the FDA. The woman says she hasn't traveled outside of the county in months.
The Red Cross said it will phase in universal testing.
Donated blood should be tested for the Zika virus, which can cause birth defects, USA regulators warned Friday amid a mounting outbreak of the mosquito-borne virus in the United States.
Her male partner had been bitten by mosquitoes during his travel but had no signs of Zika infection, which typically include rash, red eyes, fever and malaise, He told officials he had only felt exhausted, which he attributed to travel.
The nation's first local, non-travel-related infection of Zika virus occurred in Puerto Rico in December. Once infected, a person can spread it to another through sexual contact.
Most of the cases within the continental USA involved individuals who contracted the virus while traveling in another country, while most of the Puerto Rico cases were locally acquired.
Blood banks already test donations for HIV, hepatitis, West Nile and other blood-borne viruses.
Around 2,200 Zika cases have been reported in the continental US and more than 13,000 in Puerto Rico, according to the Centers for Disease Control and Prevention. But both had visited a Zika area so infection from mosquito bites couldn't be ruled out.
Two US lawmakers, Congresswoman Rosa DeLauro of CT and Congressman Lloyd Doggett of Texas, had recently urged the FDA to expand testing for Zika to blood banks nationwide, saying it would cost less than $10 per donor.
The tropical mosquito that spreads Zika and other viruses is found along the southern U.S. Friday's directive lists 11 states that will need to begin screening blood in the next month due to their location or because of the influx of travelers from Zika outbreak countries. Currently, it is conducting Zika tests in five southeastern states and will expand testing to four additional states in the south central and southwestern U.S. over the next two weeks, the organization said in a statement.
On the list: Alabama, Arizona, California, Georgia, Hawaii, Louisiana, Mississippi, New Mexico, New York, South Carolina and Texas.
Facilities in all other states should be following the new guidelines within the next 12 weeks, the FDA says.
An executive for America's Blood Centers, which has more than 600 locations in the US and Canada, warned that the amount of work needed to comply with the FDA's timeline is "titanic".
The FDA works with other federal agencies to set standards for screening, testing and handling blood donations.
Friday's announcement follows recent pressure from members of Congress to expand Zika screening.
On Friday, DeLauro applauded to decision, calling it "a strong step forward in protecting our nation's blood supply and the American people".