Constant monitoring of road traffic is important part of modern smart city systems. The proposed method estimates average speed of road vehicles in the observation period, using a passive acoustic vector sensor. Speed estimation based on sound intensity analysis is a novel approach to the described problem. Sound intensity in two orthogonal axes is measured with a sensor placed alongside the road. Position of the apparent sound source when a vehicle passes by the sensor is estimated by means of sound intensity analysis in three frequency bands: 1 kHz, 2 kHz and 4 kHz. The position signals calculated for each vehicle are averaged in the analysis time frames, and the average speed estimate is calculated using a linear regression. The proposed method was validated in two experiments, one with controlled vehicle speed and another with real, unrestricted traffic. The calculated speed estimates were compared with the reference lidar and radar sensors. Average estimation error from all experiment was 1.4% and the maximum error was 3.2%. The results confirm that the proposed method allow for estimation of time-averaged road traffic speed with accuracy sufficient for gathering traffic statistics, e.g., in a smart city monitoring station.