The boy, from Yolo County, Calif., was left at the Kimball County Hospital late Friday afternoon by his mother, who drove to Nebraska.
The boy is currently in a foster home. Nebraska officials are contacting the appropriate agencies in California.
It brought the total number of drop-offs to 27, and the total number of children left at a hospital to 36 since the law went on the books in July. Many of them were preteens or teenagers as old as 17.
Nebraska lawmakers changed the law Friday, which previously did not have an age limit for drop-offs. The change took effect Saturday.
Child experts and others worry that children old enough to be aware of what was happening to them could be scarred emotionally for life.
"They did not ask to come into this world, they did not choose the parents they may have been cursed with," Sen. Ernie Chambers said Wednesday.
However, many lawmakers, health officials and child welfare experts have been sympathetic to the parents and guardians, saying they were trying to get help for their troubled children and were not merely abandoning them.
Parents who have spoken publicly said they thought they had nowhere else to turn to get help for out-of-control, sometimes mentally ill children.
Lawmakers plan to address the lack and accessibility of services for troubled, older youths during the regular legislative session, which begins in January.