Three other people were injured when a gunman walked into the crowded synagogue with an AR-type assault rifle and opened fire on worshippers.
He was chased out of the building when an off-duty Border Patrol officer fired back at him.
Police have named the suspect as 19-year-old John Earnest.
He allegedly wrote on an online message board that he planned to live stream his attack in San Diego, which took place exactly six months after shootings at a synagogue in Pittsburgh where 11 people died.
The rabbi's hands shattered when they were hit in the gunfire.
Trump said "Synagogue shooting 'looks like a hate crime."