A probable case of local transmission of the Zika virus has been reported in Texas, state health officials announced on Monday, making it the second state, after Florida, in which the infection is thought to have been carried from person to person by mosquitoes.

The patient is a woman who is not pregnant and lives in Brownsville, on the Gulf Coast near the Mexican border. The state’s first case of chikungunya, a virus spread by the type of mosquito that carries Zika, was confirmed this year in Brownsville.

Medical investigators must now determine whether the infection is spreading and, if so, how many people may have become infected. Officials have begun asking the woman’s neighbors for urine samples and trapping mosquitoes to test for the virus.

State and county health officials are working with the Centers for Disease Control and Prevention on the case. The state medical operations center has been activated to help with contact tracing, mosquito surveillance and public education.

The C.D.C. sent a training team to Texas this year but has not yet been asked to send an emergency response team, said Dr. Thomas R. Frieden, the agency’s director.

No travel alert suggesting that pregnant women avoid the area will be issued now, Dr. Frieden said, because a single case does not constitute evidence of continuing local transmission. “Most local cases are isolated dead ends,” he said.

Confirmation of several cases within a roughly one-square-mile area for more than about two weeks, despite aggressive mosquito control, would prompt an alert from federal authorities.

In Florida this year, the C.D.C. first advised pregnant women to avoid Wynwood, the neighborhood where the first cases in Miami were discovered, and later suggested they avoid all of Miami-Dade County.

There have now been 4,444 confirmed cases of Zika infection in the continental United States, including 1,114 in pregnant women. Most of those infected had traveled to countries where the virus had been spreading, but 182 of the infections were contracted in Florida by people who had not visited such places.

The Texas patient, who was not identified, told investigators that she had not traveled recently to anywhere the virus had been spreading. She had no other risk factors, such as having sex with someone who had visited an area with Zika transmission.

“We knew it was only a matter of time before we saw a Zika case spread by a mosquito in Texas,” said Dr. John Hellerstedt, the state health commissioner.

Residents of Brownsville, a city of 183,000, are concerned but not fearful, Mayor Tony Martinez said on Monday.

“I don’t think it’s something that people need to be alarmed about, but by the same token, they need to be cautious about it and report anything that needs to be reported to our health department,” Mr. Martinez said.

“On the coast, we kind of hoped that it wouldn’t happen,” he added, “but the likelihood was pretty high.”

Dr. Carmen Rocco, a Brownsville pediatrician, said she had been checking her patients for Zika, but none so far had been infected. Most of her patients are poor enough to be on Medicaid, and she praised state health officials for reinstating a Medicaid benefit for mosquito repellent.

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“Families were taking advantage of that,” she said.

While cold weather is arriving in other parts of the country, southern Texas has had an unusually hot autumn, making it more hospitable to the Aedes aegypti mosquitoes that transmit Zika.

Even in normal years, Aedes aegypti can persist in the Brownsville area well into December, so new cases may be confirmed in January or later.

“I predicted last April that we would see cases along the Texas Gulf Coast this summer,” said Dr. Peter J. Hotez, the dean of the National School of Tropical Medicine at Baylor College of Medicine. “This is now the one case we know about, but we don’t know if there are dozens or hundreds.”

“Because of the lack of funds from Congress, there has been no active surveillance along the Gulf Coast,” he added. “Those cases in Florida were found by serendipity.”

Chris Van Deusen, a spokesman for the Department of State Health Services in Texas, said the new case was discovered because the woman fell ill and was tested for Zika infection by a local doctor, who alerted public health authorities. All such cases are investigated to see if a patient has a travel history or other risk factors that might explain the infection.

“Pregnant women should continue to protect themselves from mosquito bites there and elsewhere in Texas,” Mr. Van Deusen said.

Mosquito control measures will be stepped up, he said, but he did not know if they would involve aerial spraying of pesticides like Naled and larvicides like Bti.

In the Wynwood section of Miami, mosquito swarms did not decrease enough to stop disease transmission until both types of aerial spraying were used.

Thousands of Mexicans and Americans cross bridges over the Rio Grande each day in the Brownsville area; it is possible that the virus has been spreading in Matamoros, Mexico, just across the border.

In 2002, when there was a small outbreak of dengue in Brownsville, Dr. Hotez said, there turned out to be a much larger one in Matamoros. Both cities have poor neighborhoods where residents lack air-conditioning and window screens, he said, but many more Matamoros residents live in poverty.

“We won’t know how widespread the virus really was until babies with microcephaly begin being born, probably in the spring,” Dr. Hotez said, referring to the Zika virus and its link to the birth defect. “And I expect it to return next year.”

The C.D.C. regularly collaborates with Mexican health authorities, and Mexico “has quite a strong mosquito control program,” Dr. Frieden said.

Exactly how much Zika infection there may be in nearby parts of Mexico is unknown. “We know there is transmission in the border areas,” Dr. Frieden said. “But exactly where, we don’t know.”

A version of this article appears in print on November 29, 2016, on page A11 of the New York edition with the headline: Texas Woman Contracts Zika as Mosquitoes Spread the Virus to a Second State.