Christy Freeman, 37, has been charged with first and second-degree murder and manslaughter in connection with the death of one of the babies.
Further charges may follow, said Ocean City police spokesman Barry Neeb.
Police found the body of one baby wrapped in a blanket in Freeman's apartment on Thursday after she was admitted to a local hospital with cramps and bleeding, Neeb said.
Doctors at the hospital determined that Freeman had been pregnant but not anymore, prompting police to search her apartment.
At the apartment, police also found a garbage bag hidden in a trunk in Freeman's bedroom.
Inside were three smaller plastic bags, two of which contained the remains of two more infants, and a third contained what police said was a placenta.
The next day, the remains of a fourth infant were found in another garbage bag inside a Winnebago motor home parked in Freeman's driveway, according to a police statement.
A medical examiner's report on the ages of the infants and the cause of their deaths is expected this week.
"None of them were full-term," Neeb said.
Police are continuing to search Freeman's home and excavate its surroundings in an operation that also involves the FBI.
Freeman has four other children who are believed to be teenagers, Neeb said.
Freeman was at a bail hearing this morning, and the case is expected to be referred to a grand jury, Neeb said.