The new app, dubbed Slingshot, allows users to sign up for the service with their mobile phone number and connect with friends in their phone's contact list or, if they want, by finding their Facebook friends.
Photos on Slingshot disappear from users' phones shortly after they are viewed, reflecting a growing anxiety about privacy in the age of Internet social networking.
Facebook's release of Slingshot comes as a new crop of mobile messaging services gain popularity and threaten to draw younger users away from Facebook's 1.28 billion-user social network.
To help mitigate the threat from alternative social networks, Facebook is developing a variety of standalone apps and acquiring fast-growing rivals. In 2012 it acquired photo-sharing service Instagram and in February it announced plans to acquire messaging app WhatsApp for $19 billion.
Snapchat, an app that lets users send messages that automatically disappear after a few seconds, turned down a $3 billion acquisition offer from Facebook last year, according to media reports at the time.
Unlike other messaging apps, Slingshot will not allow users to view the messages they have received from their friends until they reciprocate and send back a photo or video of their own. The rule is designed to make Slingshot a service for which everyone contributes material, although it could require a learning curve that confuses or turns off some users.
"When everyone participates there's less pressure, more creativity and even the little things in life can turn into awesome shared experiences," Facebook said in a blog post announcing the service on Tuesday.
Slingshot will be available in the United States on Tuesday for Android and iOS devices.