Vehicular Named Data Networking (VNDN) is one of the potential and future networking architectures that could allow smart vehicles to exchange data by simply disseminating the content over the network. VNDN supports only a pull-based data forwarding model. In the pull-based mode, the content is forwarded upon request. However, in critical situations, a push-based data forwarding model is essential to design in order to broadcast the critical data packets without any requests. One of the major challenges of push-based data forwarding in VNDN is the broadcast storm effect, which occurs when a producer broadcasts critical information over the network. For instance, in emergency situations such as accidents, road hazards, rain, etc., the producer generates a critical data packet and broadcasts it to all the nearby vehicles. Subsequently, every vehicle broadcasts the same critical data packet to each other, which leads to the broadcast storm effect on the network. Therefore, this paper proposes a Fuzzy logic-based scheme to mitigate the broadcast storm effect. The novelty of this paper is the suggestion and application of a Fuzzy logic approach in order to mitigate critical data broadcasting in VNDN. In the proposed scheme, the vehicles are distributed in clusters by using the K-Means clustering algorithm, and then a Cluster Head (CH) is chosen by using a Fuzzy logic approach. The CH is responsible for broadcasting the critical data packets to all other vehicles in a cluster. A Gateway (GW) has the role of forwarding the critical data packets to the nearest clusters via their GWs. The simulation results show that the proposed scheme performs better than the naive scheme in terms of transmitted data packets and efficiency.