Vehicular networks support intelligent transportation system (ITS) to improve drivers’ safety and traffic efficiency on the road by exchanging traffic-related information between vehicles and also between vehicles and infrastructure. Routing protocols that are designed for vehicular networks should be flexible and able to adapt to the inherent dynamic network characteristics of these kind of networks. Therefore, there is a need to have effective vehicular communications, not only to make mobility more efficient but also to reduce collateral issues such as pollution and health problems. Nowadays, the use of machine learning (ML) algorithms in wireless networks are on the rise, including vehicle networks that can benefit from possible data-driven predictions. This work aims to contribute to the design of a smart ML-based routing protocol for vehicular ad hoc networks (VANETs) used to report traffic-related messages in urban environments. We propose a new ML-based forwarding algorithm to be used by the current vehicle holding a given packet to predict which vehicle within its transmission range is the best next-hop to forward that packet towards its destination. Our algorithm is based on a neural network designed from a dataset that contains data records that are captured during simulated urban scenarios. Simulation results show how our ML-based proposal improves the performance of our multimetric routing protocol for VANETs in urban scenarios in terms of packet delivery probability. The performance evaluation of MPANN shows packet losses lower than 20% (and average packet delays below 0.04 ms) for different vehicles’ densities, in completely new scenarios but of similar complexity than the Barcelona scenario used to train the model. Even for much more complex scenarios (with narrow curvy streets), our proposal is able to reduce the packet losses in 20% with respect to the multimetric routing protocol as well as the average packet delays in 0.04 ms.