The perpetrator allegedly attacked the woman when she visited a café in Djanet in southeastern Algeria on October 11. In front of her children's eyes, he cut her throat and shouted "Allahu akbar" and "long live Palestine", according to media reports.
The woman later died at the hospital.
The perpetrator fled the crime scene, but was arrested a few days later. Shortly before the murder of the Swiss woman, he allegedly attempted to attack another group of tourists at a market.
According to the Swiss Foreign Ministry, the woman was traveling in Algeria with four other Swiss citizens.
Algeria in northwestern Africa has in recent years tried to attract more tourists to the country, including by promising simplified tourist visas.