The Galveston Police Department said at about 9:45 a.m., officers responded to reports of an abandoned child in the middle of the road just outside the Kroger near 59th Street and Seawall Boulevard.
Officials said the child was still alive and was taken to the trauma center at The University of Texas Medical Branch Galveston.
In an afternoon update, Galveston police said the baby had died at the hospital.
Galveston PD has not yet been able to identify the girl but said she was about 17 months old.
"This was definitely not a natural death," Police Chief Doug Balli said during an afternoon press conference, adding that the baby had suffered trauma and other injuries likely from a fall.
The chief said a suspect has been detained and will face a capital murder charge. Police have not identified that suspect or released additional information but added that the child's family has been notified.
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