She fired at the man, killing him as he stood just inside the doorway of the apartment, police said.
The woman and the children, all of whom are under the age of 7, were not injured, the news station reported.
Police identified the dead man as Michael Hawkins. A man at the scene who identified himself as Hawkins' father told WISH-TV that his son went by the nickname Lucky.
WXIN-TV in Indianapolis reported that a neighbor said she heard the gunshots and saw a man running away from the apartment complex immediately after the shooting. A second person drove away, though police have not confirmed if either person is considered a suspect in the case.
Wednesday's shooting was the second time in two days that an Indianapolis homeowner shot and killed an intruder. A man killed Derrick Johnson Jr., 18, early Tuesday morning after the teen broke into his home through a window, WXIN-TV reported.
The man’s wife and 3-year-old child were home with him at the time of the break-in.
It was not immediately clear if charges were being considered in either case. An Indianapolis Metro Police Department spokesman said residents have a right to protect themselves in their homes.
"It is disheartening that we see burglaries resulting in death, but we live in Indiana and it's legal for people to have guns to protect themselves," Officer Aaron Hamer said.
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