Neither woman nor child has been identified in the incident that unfolded in less than 30 seconds on surveillance video, the Montgomery County Sheriff's Office said.
Texas investigates migrant child's death after US detention
The video ends with the woman getting into a car that speeds away from the scene in Spring, about 40 kilometres north of Houston.
A woman who answered the door found the child she had never seen before, along with two bags and no adult, the sheriff's office said.
"The child is uninjured and appears to be in good health," it said, adding that the boy was in the custody of Child Protective Services and was being asked who left him behind.
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