Milk-run tours with time windows are an essential strategy to collect goods to minimize production and transportation costs. Due to unexpected events at the supplier production or traffic congestion, delays can occur during the vehicle route execution, causing non-compliance between the logistics operator and the company. This paper describes the DMRVR (Dynamic Milk-Run Vehicle Routing) solution that uses a dynamic routing algorithm along with fog-based vehicular ad hoc networks for implementing the collection of goods in milk-run operations that respect the company’s time window. When a production delay occurs, the supplier sends a message through the vehicular network to alert the pickup vehicle, forcing it to make dynamic route changes to satisfy the constraints. We have implemented a queue with a timeout and retransmission features to improve the vehicular network’s message delivery. To assess the DMRVR solution, we analyzed the efficiency of the dynamic vehicle routing and the vehicular network impacts. In the experiments, we used an event-based network simulator OMNeT++ bidirectionally coupled with SUMO (Simulation of Urban Mobility), aiming to make the most realistic simulations. Simulation results show the average route time was lower than the time limit imposed by the company with the DMRVR solution. In dense vehicular network scenarios, the message delivery success rate is higher. Conversely, when the vehicular network scenario is sparse, it is necessary to balance network coverage and distribute more RSUs in specific places.