Authorities say the packages were delivered Wednesday morning to a home on Statesir Place in Middletown, Monmouth County.
The suspect parked her black Jeep Cherokee in the middle of the street, walked up the sidewalk and removed the two packages from the porch, then loaded them up and drove away.
The theft was captured on the home surveillance camera of the resident, Kristie Kane.
Middletown Police released video of the theft on their Facebook page, hoping someone will recognize the SUV and the woman, who was wearing a white hooded vest and a black shirt.
Police say a gift of baby clothes and other items were in the stolen packages sent to the mother-to-be from the grandmother-to-be.
Neighbors heard about the theft, and Thursday afternoon one saw the boxes dumped at a postal office building. Kristie drove over and found her boxes, getting her gifts back.
There were also boxes belonging to other people delivered to their addresses that had also been dumped at that box.
Anyone with information is asked to call Detective Daniel Sullivan at 732-615-2255 or Police Headquarters at 732-615-2100.