The created by games manufacturer Gamesys, will only be available in the UK, where online gambling is well regulated.
It will not appear to users who are under the age of 18 or from other countries.
The app, which launches this week, requires a £10 deposit and £30 to play, and players can chat to their friends while playing bingo.
Players enter their card details into the app, which is claimed to be "100% safe and secure".
Their activity will be shared with friends in their newsfeeds. However, it will not appear in users' newsfeeds who are under the age of 18, due to the network’s age-gating technology.
Gamesys, which operates the Sun Bingo and Heart Bingo, is one of the UK's leading gambling operators.
Facebook is talking to other games makers about introducing other gambling games, such as blackjack and roulette, according to the Financial Times.
The company said in a statement: "Real money gaming is a popular and well-regulated activity in the UK and we are allowing a partner to offer their games to adult users on the Facebook platform in a safe and controlled manner."
A Facebook spokeswoman would not confirm whether any more gambling games were in the pipeline or whether they would be introduced to other markets, such as the US, where online gambling regulation varies.
Separately, Amazon is making its first moves into social gaming and debuts its first Facebook game, as it moves to take on the likes of Zynga.
The ecommerce giant has launched Amazon Game Studios, which is a new team focused on "creating innovative, fun and well-crafted games."
It has also announced its first Facebook game, called 'Living Classics', which features animated illustrations from children's books including 'Alice in Wonderland' and 'The Wizard of Oz'. The game revolves around reuniting fox families, while earning rewards and rediscovering stories, according to Amazon.
The company said in a post that the move into games was because many of its customers enjoy playing games, including free-to-play social games, and it believes it can "deliver a great, accessible gaming experience that gamers and our customers can play any time."
An Amazon spokeswoman was not able to confirm whether its games would carry advertising.
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