Traffic census data are essential for investigating traffic volumes and vehicle movements, and count mechanization is currently the most efficient way to obtain and utilize advanced traffic census data. However, efforts to mechanize traffic censuses have not progressed significantly in Japan owing to the price of such systems, the size of the necessary equipment, and privacy issues. In this paper, we propose a novel vehicle-counting sensor system that is inexpensive and easy to set up. Our system is based on a piezoelectric vibration sensor that senses road vibrations from passing vehicles. More specifically, the system consists of (i) a vibration sensor device that we designed and prototyped in-house and (ii) a passing vehicle estimation method that determines the number of passing vehicles from the vibration sensor data. Our system, which achieves high accuracy owing to the use of machine learning (ML), makes it possible to conduct traffic censuses by simply placing the sensor on sidewalks next to the road that is being surveyed. To demonstrate the utility of our system, we conducted an experiment in which the vibration sensor was placed on a sidewalk, and then linear discriminant analysis (LDA) was used to estimate the number of vehicles that were traveling on the adjacent road using only the data collected from the vibration sensor. Our results showed that the number of passing vehicles could be estimated with an accuracy of 98.3%.