The case was reported on a Saudi Arabian news site as an example of the "strife" the social networking site is causing in the Islamic nation.
It said the man shot his daugther after discovering she had been chatting online to a young man she had met on Facebook.
“Security sources assured Al-Arabiya.net that the father beat up his daughter and then shot her dead,” it said.
A leading Saudi preacher told Al-Arabiya.net that Facebook was a "door to lust" for women and called for it to be blocked to prevent social "strife".
Sheikh Ali al-Maliki said women were posting "revealing pictures" and "behaving badly" on the site, which has become popular with young Saudis.
Internet engineers said that young Saudis were using Facebook to flirt and make "web-cam calls".
Saudi Arabia imposes an austere form of Sunni Islam which prevents unrelated men and women from mixing, bans women from driving and demands that women wear a headscarf and cloak in public.
One female Saudi Facebook fan told The Mail that blocking the site would be pointless because people would simply switch to similar sites.
The 27-year-old woman, who did not want to be named, admitted many young Saudis used Facebook to get in touch with members of the opposite sex.
“In Saudi Arabia, we live more of a virtual life than a real life. I know people who are involved in on-line romances with people they have never met in real life,” the woman said.
“And many of us use Facebook for other things, like talking about human rights and women's rights.
"We can protest on Facebook about the jailing of a blogger which is something we couldn't do on the streets."
Engineers also told Al-Arabiya.net that there were Facebook pages for homosexual and lesbian relations. Homosexuality is illegal in Saudi Arabia and is punished by flogging, jail or even death.
The Saudi authorities block access to websites they deem sexual, pornographic, politically offensive, "un-Islamic" or disruptive because of controversial religious and political content.
But Syria is the only Arab country so far to have blocked Facebook.
When the ban was enforced in December, Syrian media said it was to prevent Israeli users from infiltrating Syrian social networks.