A surge in the number of infants born with tiny brains has led Brazil’s health ministry to warn pregnant women to take extreme measures to avoid mosquito bites, which may infect them with a recently arrived virus. Some prominent obstetricians in Brazil now advise women against becoming pregnant at all.

The increase in microcephaly — an incurable form of brain damage — has been blamed on an epidemic of the Zika virus, which was unknown in Latin America before this year.

A few Zika infections have been detected in the United States in returning travelers. Those imported cases “will likely increase and may result in local spread of the virus in some areas of the United States,” the Centers for Disease Control and Prevention warned recently.

The mosquito species that transmits Zika virus are common in Florida and along the Mexican border, but the pathogen has not yet been found in them.

More than 2,700 microcephalic babies have been born in Brazil this year, up from fewer than 150 in 2014, according to news media reports in Brazil. Though the increase is tentatively blamed on spreading Zika virus, some say the link is not clear.

“We don’t know if it’s only Zika or if it’s a combination of Zika, dengue and chikungunya,” said Dr. Marco Collovati, the founder of OrangeLife, a Brazilian diagnostics company that is working on a rapid test for the virus. “Maybe a woman was infected by dengue a year before, and now is pregnant and gets Zika.”

Microcephaly is often not detectable by ultrasound during pregnancy before the third trimester. Abortion is illegal in Brazil.

Zika fever emerged in Africa decades ago — it is named after the Ugandan forest where it was discovered in monkeys in 1947 — and has long circulated in Asia. The virus began appearing on South Pacific islands in 2007 and emerged in Brazil early this year, said Scott C. Weaver, the director of the Institute for Human Infections and Immunity at the University of Texas Medical Branch in Galveston.

Zika is from the same family of mosquito-borne viruses as dengue, chikungunya, West Nile and yellow fever, and the symptoms of infection — fever, rash and joint pain — are similar. Only a few top Brazilian laboratories can test for Zika, so a diagnosis is often made only by first eliminating other possibilities like dengue. There is no treatment.

The suspected connection between Zika and microcephaly emerged in the past few weeks. After an outbreak in French Polynesia in 2013, researchers have suspected that Zika also leads to Guillain-Barré syndrome in adults, in which muscle weakness may evolve into paralysis.

Because of El Niño this year, Brazil’s weather has been unusually hot and rainy, and it will probably grow hotter, with more mosquitoes before the Olympics begin this summer. “So as you can see, it’s a big, big mess,” Dr. Collovati said.