Railroads are a critical part of the United States’ transportation sector. Over 40 percent (by weight) of the nation’s freight is transported by rail, and according to the Bureau of Transportation statistics, railroads moved $186.5 billion of freight in 2021. A vital part of the freight network is railroad bridges, with a good number being low-clearance bridges that are prone to impacts from over-height vehicles; such impacts can cause damage to the bridge and lead to unwanted interruption in its usage. Therefore, the detection of impacts from over-height vehicles is critical for the safe operation and maintenance of railroad bridges. While some previous studies have been published regarding bridge impact detection, most approaches utilize more expensive wired sensors, as well as relying on simple threshold-based detection. The challenge is that the use of vibration thresholds may not accurately distinguish between impacts and other events, such as a common train crossing. In this paper, a machine learning approach is developed for accurate impact detection using event-triggered wireless sensors. The neural network is trained with key features which are extracted from event responses collected from two instrumented railroad bridges. The trained model classifies events as impacts, train crossings, or other events. An average classification accuracy of 98.67% is obtained from cross-validation, while the false positive rate is minimal. Finally, a framework for edge classification of events is also proposed and demonstrated using an edge device.