Center of device & radiological health (CDRH) definition of a general wellness products as
“Products that are intended for only general wellness use and present a low risk to the safety of the user.”
Based on this definition, I do not believe that the fitbit is required to have FDA approval because it is used to track your heart rate as a wellness product rather than a device. Since it is not a device it does not have to comply with the FDA requirements. The fitbit is used to promote healthy activity, it does not state claims of life sustaining or improving health. Even though the slogan states “every beat counts” it does not imply that it is going to help monitor someone’s health.
If the FDA were to consider the fitbit a device then I would classify it as a class 2. The fitbit is very similar to an EKG because they both monitor heart rate. The fitbit would need clinical trials to test if the device is accurate. A class 2 device would need the investigational device exemption (IDE) and a 510k form.

Reference:
http://www.fda.gov/downloads/medicaldevices/deviceregulationandguidance/guidancedocuments/ucm429674.pdf