Helsinki-based ProtoGeo created the Moves app that uses a smartphone's built-in sensors to track activity and calories burned.
The acquisition offers the social network an entry into the burgeoning health technology market.
Other recent purchases include mobile messaging firm WhatsApp and virtual headset maker Oculus.
Facebook did not reveal how much it paid for ProtoGeo, which has fewer than 10 employees, but it is believed to be a fraction of the price it has paid for more high-profile firms recently.
It paid $2bn (£1.1bn) for Oculus VR and spent $19bn (£11.3bn) on WhatsApp.Targeted ads
In a blogpost the fitness firm moved to reassure its users about the purchase.
"For those of you that use the Moves app - the Moves experience will continue to operate as a stand-alone app, and there are no plans to change that or co-mingle data with Facebook."
Meanwhile Facebook said of the purchase: "The Moves team has built an incredible tool for the millions of people who want to better understand their daily fitness activity, and we're looking forward to the app continuing to gain momentum."
The app runs in the background of users' phones, using location data to monitor activities through the day.
The free app has been downloaded more than four million times for both iPhone and Android phones, according to the firm.
Many of the big technology firms are seeing money to be made from health technology. There is a range of fitness bands and smartwatches on the market already.
Apple is rumoured to be on the verge of launching its own smartwatch with fitness features and Google last month launched software for wearables.
But for Facebook, the purchase of a fitness app is likely to be all about new data which will allow it to better target adverts, thinks Alys Woodward, an analyst with research firm IDC.
"They want to know more stuff about what people do and where they are. This is useful information even if they don't tie it back to the individual," she said.