Older adults are more vulnerable to falling due to normal changes due to aging, and their falls are a serious medical risk with high healthcare and societal costs. However, there is a lack of automatic fall detection systems for older adults. This paper reports (1) a wireless, flexible, skin-wearable electronic device for both accurate motion sensing and user comfort, and (2) a deep learning-based classification algorithm for reliable fall detection of older adults. The cost-effective skin-wearable motion monitoring device is designed and fabricated using thin copper films. It includes a six-axis motion sensor and is directly laminated on the skin without adhesives for the collection of accurate motion data. To study accurate fall detection using the proposed device, different deep learning models, body locations for the device placement, and input datasets are investigated using motion data based on various human activities. Our results indicate the optimal location to place the device is the chest, achieving accuracy of more than 98% for falls with motion data from older adults. Moreover, our results suggest a large motion dataset directly collected from older adults is essential to improve the accuracy of fall detection for the older adult population.