Indianapolis police said responding officers found two men shot at the scene, an apartment complex on the city's Near Northside, and EMS officials declared one of them dead Tuesday, the Indianapolis Star reported.
Police also said the deceased was holding his baby daughter in his hands when he was shot.
The baby was taken to an area hospital, where doctors said she wasn't seriously hurt, the Star said.
Police haven't identified any suspect so far.
The Star said the shooting death was the fifth in as many days in Indianapolis.