Two videos showing the child's death were posted on the man's Facebook page for about 24 hours, Reuters reported. They were taken down about 5 p.m., according to Reuters.
Thailand's Ministry of Digital Economy told the news agency it requested Facebook remove the videos.
The man killed himself, Reuters wrote.
Several dozen people, including the girl's mother, attended the baby's funeral on Tuesday.
"This is an appalling incident and our hearts go out to the family of the victim. There is absolutely no place for acts of this kind on Facebook," a company spokeswoman said.
The incident comes a week after an Ohio man fatally shot a man walking down the street and uploaded the video to Facebook. He later killed himself after a police pursuit in Pennsylvania.
The slaying prompted Facebook CEO Mark Zuckerberg to say at a developer's conference: "We have a lot of work, and we will keep doing all we can to prevent tragedies like this from happening."