People could access the videos of the child's murder on her father's Facebook page for roughly 24 hours, until they were taken down around 5 pm in Bangkok (1000 GMT) on Tuesday, or about a day after being uploaded.
Last week, Facebook said it was reviewing how it monitored violent footage and other objectionable material after a posting of the fatal shooting of an elderly man in Cleveland, Ohio was visible for two hours before being taken down.
The harrowing footage from Thailand shows Wuttisan Wongtalay tying a rope to his daughter's neck before dropping her from the rooftop of a deserted building in the Thai seaside town of Phuket.
Wuttisan's suicide was not broadcast but his lifeless body was found beside his daughter, said Jullaus Suvannin, the police officer in charge of the case.
"He was having paranoia about his wife leaving him and not loving him," Jullaus told Reuters.
Reuters was unable to contact the mother of the dead child. Calls to her mobile number went unanswered. Television images showed her weeping and holding the dead baby.
A regional Facebook representative in Singapore was not immediately available to comment.
After the company faced a backlash for showing the video of the Cleveland killing, Chief Executive Mark Zuckerberg said Facebook would do all it could to prevent such content in the future.
Thai netizens voiced outrage about the clips showing the child's killing.
"This is the most evil clip I've seen in my life," said one user, Avada Teeraponkoon. "I couldn't stand it for more than one second."
"How can he watch his own child stop breathing?" said another, Rujirek Polglang. "He should have just died alone."
The killing was the first in Thailand known to be broadcast on the social networking site, said Thai deputy police spokesman Kissana Phathanacharoen.
"It could be influenced by behavior from abroad, most recently in Cleveland," Kissana told Reuters.
Before they were taken down, the first video had drawn 112,000 views by mid-afternoon on Tuesday, while the second video showed 258,000 views.
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)