The match, between Atletico Madrid and Athletic Club, will be streamed on the popular social media site on Saturday 28th May at 9:45 am GMT.
Atletico Madrid is currently third in the league, while Athletic is first.
The online broadcast will have TV quality, and the match will be available to every country in the world.
It comes after BT announced that it would show the men's Europa and Champions League finals live on YouTube for free as well as its TV channel and website.
The strategy turned out to be a ratings success for the Europa final, which took place on the 18th of May. It prompted YouTube to confirm it would not make a bid for the rights to Premier League games in the near future.
Gareth Capon, CEO of Grabyo - a mobile advertising company partnering with LaLiga - said, that live streaming was the most important trend in social media:"Live streaming is the most important trend in social media:
La Liga broadcasting a competitive fixture to Facebook is a great example of major sports rights holder using the reach, engagement and viral distribution on social media platforms to distribute their content.
The global shift towards fans consuming content on their mobile devices is driven by social platforms with video driving greatest engagement for fans around the world.
The Primera Division, the La Liga equivalent for Spanish women's football, was founded in 1988 as the Liga Nacional. FC Barcelona has won the title for the last four years in a row, and is currently second behind Athletic Club.