Health officials made the grim announcement as the state reported a record 174 new coronavirus deaths on Friday, numbers that are expected to climb further still. It was the third consecutive day the state recorded more than 100 deaths.
“We currently have 85 babies under the age of one year in Nueces County that have all tested positive for Covid-19,” said Annette Rodriguez, director of public health for Corpus Christi Nueces County.
"These babies have not even had their first birthday yet. Please help us stop the spread of this disease," she added.
More than 3,700 Texans have died so far of the coronavirus. Some hospitals are now reporting shortages of intensive care unit beds for infected patients.
Dr Alison Haddock of the Baylor College of Medicine told the Associated Press that the current situation is worse than after Hurricane Harvey, which swamped Houston with floodwaters in 2017.
"I've never seen anything like this COVID surge," said Dr Haddock, who has worked in emergency rooms since 2007. "We're doing our best, but we're not an ICU."
Patients are waiting "hours and hours" to get admitted, she said, and the least sick people are lying in beds in halls to make room for most seriously ill.
Texas was one of the first states to reopen following a nationwide shutdown implemented to contain the virus. Governor Greg Abbott gave the go-ahead for businesses, including bars and restaurants, to reopen in May.
After initially resisting mandates for people to wear masks, Mr Abbott issued a statewide order earlier this month that requires Texans living in counties with more than 20 coronavirus cases to wear one while in frequenting a business and public buildings.
Texas is not alone in struggling to contain the spread of the virus. Eighteen US states were this week classified as being in the “red zone” — areas reporting 100 new cases per 100,000 people per week.
According to a leaked document, which was prepared by the White House coronavirus task force and obtained by the Washington, DC-based nonprofit Centre for Public Integrity, the classification requires those areas to implement stricter public health measures to stop the spread.
Alabama, Arizona, Arkansas, California, Florida, Georgia, Idaho, Iowa, Kansas, Louisiana, Mississippi, Nevada, North Carolina, Oklahoma, South Carolina, Tennessee, Texas and Utah were named as red zone states.
The same document listed 11 states with positivity rates above 10 percent, which would also classify them as red zones: Alabama, Arizona, Florida, Georgia, Idaho, Louisiana, Mississippi, Nevada, South Carolina, Texas and Washington.
More than 3.5 million Americans have contracted the coronavirus, according to the Centres for Disease Control and Prevention. And more than 137,000 have lost their lives.
— With agencies