An autonomic network management system (ANMS) is expected to play a significant role in fifth and sixth-generation (5G and 6G) networks. It enables the network to manage itself with minimum or no human intervention. Recently, an ANMS architecture called multi-agent-based network automation of the network management system (MANA-NMS) architecture was presented. The article discussed a multi-agent service decomposition architecture, defining atomic network-functions (ANFs). These ANFs are proposed to be intelligent and autonomous agents. The agents are designed as independent atomic decision elements incorporating machine learning (ML) as an internal cognitive component. The atomic units are used as a building block for an ANMS. In line with this approach, this article proposes a network traffic classifier agent (NTCA) as a part of the network traffic management system. We first design and implement a NTCA using an ML algorithm as a cognitive component of the agent. To compare, we used K-Nearest Neighbors (K-NN), Decision Tree, Support Vector Machine (SVM), and Naive Bayes in the agent design. We perform an evaluation using classification accuracy, training latency, and classification latency. Finally, we tested the performance of the NTCA by implementing it in the MANA-NMS conceptual framework. The results show that the Decision Tree NTCA has the highest mean classification accuracy, the least mean training latency, and the lowest mean classification latency.