The new service means Messenger users will be able to ask for an Uber vehicle without leaving the Facebook software.
Users will not need to download the Uber app separately.
“Uber on Messenger” began in parts of the US this week, the two firms said.
The companies announced their new venture via separate blogs.
Facebook has some 1.5 billion users globally and Uber is the world’s biggest driver-hailing app in terms of financing.
If successful, the partnership between the firms will give Uber access to many new and potential clients – Facebook’s Messenger app has some 700 million users worldwide.
“With the ability to request, view, and pay for an Uber ride in Messenger, taking your next ride is as simple as sending a message,” Uber said on its news blog.
“You can request a ride from a car service without ever needing to download an extra app or leave a conversation,” Facebook explained.
The social media giant said the new transportation function on its Messenger app was part of its ongoing development.
“More countries and other transportation partners will be available soon,” it added.
Facebook also said the service would be “super easy”.
“Driver status updates and payment receipts will get delivered to a private conversation between you and Uber,” the firm explained.
“With everything in one place, you can seamlessly keep track of your ride and payment history.”
Uber and Facebook said they would offer users their first ride for free – for a trip worth up to $20 (£13.37). Facebook said the offer would be in place for a limited time.
In April, the social media giant removed its instant messaging service from its main mobile app and said users would have to download the Messenger app in order to send and receive messages on their smartphones.
San Francisco-based Uber was founded six years ago. It has operations in about 60 countries but has faced opposition in various parts of the world.
Earlier this year, Facebook bought the messaging service WhatsApp for $19bn (£11bn).