Algerian newspapers on Saturday said Talal Ibn Abd al-Aziz al-Rashid died in an ambush on Thursday in which nine people were killed and several others injured.
The attack is believed to have been carried out by the Salafist Group for Preaching and Combat (SGPC).
The SGPC is recently known for the kidnapping of more than 30 European tourists sightseeing in the desert earlier this year.
The group is fighting to set up a purist Islamic state and recently pledged its allegiance to the al-Qaida network, which the United States blames for the attacks on 11 September 2001, as well as many bomb attacks.
The hunting party was attacked in the region of Djelfa, 250km south of the capital Algiers, sources told the newspapers. It was not immediately clear if the victims were guides, Saudis or security forces accompanying the hunting group.
The Interior Ministry was not available for comment.
Saudi-owned newspaper Asharq al-Awsat said his body was flown to Riyadh late on Friday for burial on Saturday. Al-Rashid was a businessman and popular poet who set up a literary
magazine, al-Fawasil, 10 years ago.
Two off-road jeeps were stolen in the attack. The Algerian desert is a popular destination for Saudis hunting game, including gazelles.