Motion-based fall detection systems are concerned with detecting falls from vulnerable users, which is typically performed by classifying measurements from a body-worn inertial measurement unit (IMU) using machine learning. Such systems, however, necessitate the collection of high-resolution measurements that may violate users' privacy, such as revealing their gait, activities of daily living (ADLs), and relative position using dead reckoning. In this paper, we investigate the application of multi-party computation (MPC) to IMU-based fall detection for protecting device measurement confidentiality. Our system is evaluated in a cloud-based setting that precludes parties from learning the underlying data using multiple, disparate cloud instances deployed in three geographical configurations. Using a publicly-available dataset, we demonstrate that MPC-based fall detection from IMU measurements is practical while achieving state-of-the-art error rates. In the best case, our system executes in 365.2 milliseconds, which falls well within the required time window for on-device data acquisition (750ms).