The baby boy was six weeks old.
"Our deepest condolences go out to his parents and family," the Nueces County Public Health District said in a statement.
District director Annette Rodriguez said the child had a co-infection and his death was identified as sudden infant death syndrome, also known as SIDS, the Corpus Christi Caller-Times reported.
The baby tested positive for the virus that causes COVID-19. The child was sent home from the hospital after responding to a doctor's care.
Since the child was diagnosed with COVID-19, his death will be considered coronavirus-related.