Police say Chrissie Williams was arrested on Tuesday night in Philadelphia.
Norristown police say they tried to speak with her after her arrest but she was not cooperative.
They are preparing child endangerment charges for Tuesday's incident.
The child was found in a lot at the Central Montgomery County Mental Health and Mental Retardation Center in the 1100 block of Powell Street.
That's where staffers saw an unattended stroller with the small boy inside.
Those staffers checked with patients and visitors for information on the child and, finding none, contacted police.
Officers took the boy, believed to be six months to one year old, to the county health department for a checkup.
The boy appeared to be healthy and cared for, police said.
A duffel bag was found at the same location where the boy was found, and police say that led them to the identity of Williams.