In a statement, Nueces County’s health department said the newborn died in Corpus Christi on Thursday.
He was said to have been less than 6 months old, and no further information has been released.
“Our deepest condolences go out to his parents and family,” the Nueces County Public Health District said in a statement.
Nueces County commissioner John Marez said on social media that the newborn had been as young as six weeks old.
“My prayers and condolences go out to this baby’s family and all health care professionals involved,” added Mr Marez.
District director Annette Rodriguez said the child’s death had been diagnosed as sudden infant death syndrome, also known as SIDS, the Corpus Christi Caller-Times reported.
She added that an autopsy would be carried-out on the newborn and completed within the next 10 weeks.
“Unfortunately it does not discriminate, it affects people with comorbidities, and with pre-existing conditions like diabetes, hypertension and obesity, but now it affects everybody,” Nueces County medical examiner Dr. Adel Shaker told CNN.
”Nobody is secluded from infection,” he added.
A woman who told KRIS-TV that the newborn was her nephew, also said he was six weeks old.
“I want people to know that even if you have no symptoms like baby Isaiah did, you could still have the virus,” said Jacqueline Cruz. “He tested positive and had a fever but was released because the fever had subsided.”
She told the news station that Isaiah’s mother had been told the newborn “wasn’t breathing any longer” on Thursday.
The newborn’s death comes as more than 8,000 new Covid-19 cases were seen in Texas on Sunday, with 80 lives lost in the state.