Assessments of postural sway are associated with disease status and fall risk in Persons with Multiple Sclerosis (PwMS). However, these assessments, which leverage force platforms or wearable accelerometers, are most often conducted in laboratory environments and are thus not broadly accessible. Remote measures of postural sway captured during daily life may provide a more accessible alterative, but their ability to capture disease status and fall risk has not yet been established. We explore the utility of remote measures of postural sway in a sample of 33 PwMS. Remote measures of sway differed significantly from lab-based measures, but still demonstrated moderately strong associations with patient reported measures of balance and mobility impairment. Machine learning models for predicting fall risk trained on lab data provided an AUC of 0.79, while remote data only achieved an AUC of 0.51. Remote model performance improved to an AUC of 0.74 after a new, subject-specific k-means clustering approach was applied for identifying the remote data most appropriate for modelling. This cluster-based approach for analysing remote data also strengthened associations with patient-reported measures, increasing their strength above those observed in the lab. This work introduces a new framework for analysing data from remote patient monitoring technologies and demonstrates the promise of remote postural sway for assessing fall risk and characterizing balance impairment in PwMS.