Major Tom Effler said deputies were called to a home at 134 Jasmine Lane in Fremont at 7:34 a.m.
They found 19-year-old Cquashanda Laquan Mitchell shot to death and 56-year-old Robert Earl Mitchell wounded. Mitchell was taken to Wayne Memorial Hospital.
Effler said Rici Antonio Mitchell was taken into custody at the home.
Effler said the incident appears to the result of a domestic dispute and deputies aren't looking for any other suspects.