More than 80 babies have tested positive for coronavirus in the same county.
County public health officials made the announcement at a meeting on Friday, as Texas continues to see an uptick in cases of the novel virus.
"These babies have not even had their first birthdays yet," public health director Annette Rodriguez said. "Please help us to stop the spread of this disease.”
She urged citizens to adhere to safety guidelines.
Rodriguez added: “Stay social distanced from others; stay protected. Wear a mask when in public and for everyone else please do your best to stay home."
No further information regarding the health status of the infants was disclosed.
Nueces County, located on the Gulf Coast, has seen cases of the virus explode in the last few weeks.
“Nueces County has the fastest growth in new cases on the seven-day average than any other metropolitan county in the state," Peter Zanoni, the Corpus Christi city manager, told CNN.
On Thursday, Texas set a record with 15,038 new cases in a single day, according to data reported in The New York Times.
In addition, over 1,000 inmates of the Federal Correctional Institute at Seagoville, Texas, as well as 10 of the prison's staff members, have also recently tested positive for COVID-19.
As the cases continue to increase across the state, many are facing the pandemic without health coverage.
More than 600,000 Texans have lost their health insurance since the start of the COVID-19 outbreak, and the state now leads the country in the percentage of residents without coverage.