Parkinson's disease (PD) is a chronic movement disorder that produces a variety of characteristic movement abnormalities. The ubiquity of wrist-worn accelerometry suggests a possible sensor modality for early detection of PD symptoms and subsequent tracking of PD symptom severity. As an initial proof of concept for this technological approach, we analyzed the U.K. Biobank data set, consisting of one week of wrist-worn accelerometry from a population with a PD primary diagnosis and an age-matched healthy control population. Measures of movement dispersion were extracted from automatically segmented gait data, and measures of movement dimensionality were extracted from automatically segmented low-movement data. Using machine learning classifiers applied to one week of data, PD was detected with an area under the curve (AUC) of 0.69 on gait data, AUC = 0.84 on low-movement data, and AUC = 0.85 on a fusion of both activities. It was also found that classification accuracy steadily improved across the one-week data collection, suggesting that higher accuracy could be achievable from a longer data collection. These results suggest the viability of using a low-cost and easy-to-use activity sensor for detecting movement abnormalities due to PD and motivate further research on early PD detection and tracking of PD symptom severity.