The coronavirus disease 2019 (COVID-19) pandemic has broad negative impact on physical and mental health of people with chronic neurological disorders such as multiple sclerosis (MS). We present a machine learning approach leveraging passive sensor data from smartphones and fitness trackers of people with MS to predict their health outcomes in a natural experiment during a state-mandated "stay-at-home" period due to a global pandemic. Using data collected between November 2019 and May 2020, algorithm detects depression with an accuracy of 82.5% (65% improvement over baseline; f1-score: 0.84), high global MS symptom burden with an accuracy of 90% (39% improvement over baseline; f1-score: 0.93), severe fatigue with an accuracy of 75.5% (22% improvement over baseline; f1-score: 0.80), and poor sleep quality with an accuracy of 84% (28% improvement over baseline; f1-score: 0.84). Our approach could help clinicians better triage patients with MS and potentially other chronic neurological disorders for interventions and aid patient self-monitoring in their own environment, particularly during extraordinarily stressful circumstances such as pandemics that would cause drastic behavioral changes.