20-day-old Jomaa al-Batran was found with his head as "cold as ice" early on Sunday, his father, Yehia, said.
The baby's twin brother, Ali, was moved to intensive care at Al-Aqsa Martyrs Hospital.
The boys' father said they were born one month premature and spent just a day in the hospital, which like other healthcare centres in Gaza is overwhelmed and only partially functioning.
He said medics told their mother to keep the newborns warm, but it was impossible because they live in a tent and temperatures regularly drop below 10 degrees Celsius at night.