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.
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."
Reuters said two videos were posted, at 16:50 (local time) and 16:57 on Monday, and were taken down at about 17:00 on Tuesday, roughly 24 hours later. Facebook has yet to confirm the times to the BBC.
Thailand's ministry of digital economy said it had contacted Facebook on Tuesday afternoon about removing the videos.
Ministry spokesman Somsak Khaosuwan told Reuters: "We will not be able to press charges against Facebook, because Facebook is the service provider and they acted according to their protocol when we sent our request. They co-operated very well."
YouTube said it had taken down the video within 15 minutes of being told of its presence by the BBC.
Its statement read: "YouTube has clear policies that outline what's acceptable to post and we quickly remove videos that break our rules when they're flagged."
Shortly before the BBC alerted YouTube, the video was showing 2351 views.
Thai social media users reacted with anger to the footage, while offering condolences to the family of the girl, the BBC has reported.
Devastated relatives of the child, including the mother, picked up the body of the girl and her father from hospital on Tuesday.
Following the US killing, Facebook said it was "constantly exploring ways that new technologies can help us make sure Facebook is a safe environment".
"We prioritise reports with serious safety implications for our community, and are working on making that review process go even faster," blogged one of its executives last week.