Paramedics and police were called to the Indianapolis apartment after the woman's uncle saw one of the dead children lying on a couch.
Edyan Farah, 28, told police she was "not in her right mind," a police report said.
She allegedly explained that she had locked her children -- a seven-year-old girl, five-year-old twin girls, a three-year-old boy and an 11-month-old baby -- in the closet of an upstairs bedroom at about 6:00 am Monday.
The crowded closet was filled with clothing and other items and is about two feet wide (60 centimeters) and six feet (1.8 meters) long.
She then "placed a large bed in front of the door so that the children could not get out" and went downstairs to talk to her neighbor, the report said.
Farah allegedly told detectives that she returned to the apartment at about 4:20 pm and found her five-year-old daughter Zuhur and three-year-old Zakariya "were stiff and unresponsive."
She allegedly carried the girls downstairs and they lay there for more than four hours until her neighbors -- disturbed by her behavior and refusal to let them inside -- called her uncle.
"This case is extremely disturbing and very, very, sad," said Indianapolis police Sergeant Linda Jackson. The cause of death was not immediately known.
The surviving children were examined at hospital and are currently under the care of protective services, Jackson told AFP."Initial reports from the scene indicated that they were very thin and perhaps were malnourished," she said.
Farah faces two preliminary charges of neglect of a dependant causing death and could face further child abuse charges, she added.
Farah is a Somali immigrant and her husband was out of the country at the time of the incident. He immediately made arrangements to return when notified of the death of his children.
Formal charges are expected at a court hearing Thursday, a spokeswoman for the prosecutor's office said