Police in the Dayton suburb of Kettering say the caller told them he saw the woman Thursday.
Officer Michael Burke says authorities used a licence plate number to track down 39-year-old Genine Compton.
He said the woman told officers she was breast-feeding and wouldn't let her child go hungry.
Burke said the legal concern is that Compton had a child in her lap while driving, not that she was breast-feeding in public.
He said the child was under two years old.
Police say the woman faces up to 180 days in jail and a $1,800 fine if convicted of the misdemeanour.