An Ashkelon resident shot his infant son, 15-year-old daughter and 35-year-old wife before attempting to kill himself in the city's Sohnut Yehudit Street on Sunday afternoon.
The infant was killed from a gunshot wound to the head. The daughter and mother were reported in critical condition and connected to a respirator.
Conflicting reports indicated the man was either in critical condition or dead.
All the wounded were evacuated to Ashkelon's Barzilai Hospital.
Police were investigating the incident.