Canadian police are investigating what appeared to be a murder-suicide after a man announced on Facebook that he had killed his daughter, wife and sister, before burning himself to death.

Randy Janzen wrote on the social network on Thursday that he had killed his 19-year-old daughter Emily because of lifelong migraines that made her depressed.

Killed: Randy Janzen's wife Laurel and his daughter Emily.

In the post, which was made around noon, Janzen said that he then killed his wife because "a mother should never have to hear the news her baby has died," and his sister, so she could avoid the shame of his murderous actions.

He continued: "I have done some of the worst things I could have ever imagined a person doing. First, to do with my dear, sweet, loving daughter Emily.