The al-Arabiya Web site said the case was reported by a Saudi Arabian news site as an example of the "strife" Facebook has caused Saudi Arabia, The Daily Telegraph reported Monday.
The Web site became the subject of controversy in Saudi Arabia after preacher Ali al-Maliki labeled it a destructive force against Islam.
"Facebook is a door to lust and young women and men are spending more on their mobile phones and the Internet than they are spending on food," he said.
The Saudi news site said the Riyadh woman was beaten and shot by her father after he discovered her engaging in an online conversation with a man on Facebook. The incident occurred last August but was not reported until rafter Maliki criticized the social networking site.