Alfreda Giedrojc of Oak Lawn, Ill., was charged with first-degree murder and ordered held without bond in the death of Vivian Summers.
Prosecutors say the 62-year-old grandmother allegedly struck the infant on the head with a sledgehammer and then took a carving knife from the kitchen and slit the child's throat on Sunday.
The Chicago Tribune said Giedrojc stood silent and impassive as prosecutors described the gruesome details.
Oak Lawn police said they were called to the home on a report of an "armed subject."
Prosecutors said the child's father had left the infant in the care of Giedrojc and her husband Sunday morning while he worked with his brother-in-law on rehabbing a nearby house. The attack occurred when Giedrojc's husband went across the street to check on their work, the newspaper said, leaving Giedrojc alone with the infant.