Agriculture is a fundamental pillar of society, bearing a crucial role in shaping the economy of the country and provides huge financial prospects and the possibility of employment to the large mass of the country. Thus, the incorporation of modern technology would lead to amplification in productivity and economic escalation. In this perspective, Wireless Sensor Network (WSN) can provide a greater service by sensing, monitoring and supplying continuous information about climatic conditions like temperature, light, soil moisture, humidity, and so on. These parameters help in increment of productivity in terms of quantity and quality growth in agriculture. However, WSN brings security threats like masquerading, alteration, interference, interception, and so on, that harmfully affect crop production and other agricultural practices. Thus, privacy preservation and security enhancement for agricultural WSN are the major challenges to be conquered. To meet this purpose, a privacy-preserving efficient and secure remote user authentication scheme is introduced in this research work for the application of agricultural WSN. The proposed scheme is formally evaluated using probabilistic Random-Oracle-Model (ROR) for proving the robustness of the scheme. Further, the scheme is simulated using a well-accepted AVISPA tool to show the security strength of it. The performance analysis of our scheme shows that along with its robustness in terms of security, the proposed scheme is more efficient in terms of computation and communication overheads in contrast to other existing schemes. These aforesaid features make the proposed scheme implementable in a practical environment.