It happened at a home in the 400-block of Macon Street around 8 a.m.
Investigators charged Arin Tavon Futrell, 21, of Durham with felony negligent child abuse resulting in bodily injury. He was also arrested on outstanding warrants charging him with attempted breaking and entering and conspiracy to commit breaking and entering.
Investigators said the shooting appeared to be an accident. It happened on a porch outside a house.
A witness told ABC11 he heard Futrell and a woman arguing on the porch before the gun went off. Futrell then allegedly drove off.
Investigators say they recovered the gun.
The baby was taken to Duke Regional Hospital. Her injuries did not appear to be life threatening.