Developing technology, renders external factors possibly changing faster, while enabling managers to execute their operations more effectively and efficiently, and reflect to the changes more quickly. Today, in many industries, it has become a necessity to carry out dynamic policies for operations conducted in many areas, including logistics. In this context, in recent years, Dynamic Vehicle Routing Problems, in which decisions in vehicle routing problems are updated depending on the changes during transportation, have started to be the subject of an increasing number of academic studies. In Dynamic Vehicle Routing Problems, decision support models have been developed so far that take into account the dynamic changes of two basic parameters, demand and travel time. It is clear that a change in demand (e.g., a change in the amount of demand, a complete disappearance of demand, or the emergence of new demand points) will require updating routing decisions. However, travel time is another parameter that is equally important and may require updating in decisions. Increased travel time (i.e., reduced vehicle speed) can cause to miss customer service time windows, increase fuel and personnel costs, or lead to customer dissatisfaction. In addition, travel times are directly related to traffic density, an important social sustainability criterion. Traffic density is a parameter that affects the quality of life of a large part of the society, especially in urban transportation in big cities, and is a parameter that is considered important by the society. In many big cities, lawmakers are trying to take measures to prevent traffic congestion. Among these measures, there are practices such as restricting the entrance of commercial vehicles to busy areas, introducing additional taxes or encouraging public transportation. However, these applications have not yet become widespread in all cities where traffic problems are experienced, and they cannot completely solve traffic problems where they are applied. A clear social sustainability objective for businesses engaged in urban transport activities is to contribute minimally to increased city traffic. In this study, a dynamic, capacity-constrained vehicle routing problem is addressed, in which environmental and social sustainability aspects are considered. In the problem, it is assumed that when a vehicle arrives at a customer, instantaneous travel times and traffic density percentage estimates are updated, and new decisions are made with the current parameters. Estimated travel time and percentage of traffic density between two given points are provided by many commercial software today. The environmental sustainability component is incorporated by determining the objective function of the problem as fuel consumption minimization. The social sustainability component is incorporated by restricting the use of the routes that are expected to exceed a certain traffic density level. In this context, a threshold level was determined and any vehicle was prevented from using the arcs where the traffic density percentage estimation exceeds this threshold level. The addressed problem was modeled by the Integer Programming method, and the model was coded in C++ using the libraries of the IBM ILOG CPLEX software. In order to exemplify the applicability and academic/practical contribution of the model, a hypothetical problem was created and solved. In this context, the problem with the code “UK15_01” in the “The Pollution-Routing Problem Instance Library” library where sample routing problems are presented (http://www.apollo.management.soton.ac.uk/data15/ UK15_01.txt), is turned into a hypothetical urban routing problem by diving the distances by four. In the exemplar problem solution, it is observed that 52% of the decisions (i.e., the arcs used) obtained by statically solving the problem are changed in the dynamic solution, and it is observed that an extra vehicle is employed in order to avoid contributing to heavy traffic. Similarly, it has been observed that 33% of routing decisions are different in the proposed model when compared to the solution obtained without the social sustainability (preventing access to arcs with high traffic density) constraint. When the relevant constraint was removed, it was observed that 11% of the trips between customer pairs were on the arcs that exceeded the determined 70% density threshold. This constraint completely prevented the company from directly increasing the traffic density on these routes, but ended up with approximately 3% higher fuel consumption. The solutions obtained in the sample problem involve promising results regarding the added value that the proposed model can potentially provide, and demonstrate that environmental and social gains are possible if the model is used in practice.