The 21-year-old hanged his daughter, and then himself, at a deserted hotel in Phuket on Monday, reportedly after an argument with his wife.
Facebook sent condolences to the family for the "appalling" incident and said that the content had now been removed.
The company pledged a review of its processes after footage of a US killing stayed online for hours this month.
The footage of the Thai killing had also been available on video sharing website YouTube, but the company took it down after the BBC alerted it to its presence.
Social media anger
Relatives of the Thai man, Wuttisan Wongtalay, saw the distressing footage and alerted the police - but the authorities arrived too late to save him and his daughter.
In a statement, a Facebook spokesperson said: "This is an appalling incident and our hearts go out to the family of the victim. There is absolutely no place for content of this kind on Facebook and it has now been removed."