Understanding the time-dependent deformation of cementitious materials is crucial for predicting the long-term durability of concrete structures. Although limestone calcined clay cement (LC3) is a promising low-carbon alternative to portland cement, its long-term creep behavior at the nanoscale remains unclear. In this study, the viscoelastic properties of LC3 pastes were investigated and compared with ordinary portland cement (OPC). A phase-resolved nanoindentation creep testing was employed to characterize specific microstructural phases, and the experimental data were analyzed using the Burgers viscoelastic (BV) model. The results indicate that the hydration process of LC3 significantly increased both the reduced modulus and hardness, and these changes were well correlated with macroscopic strength development. Extending the holding time effectively stabilized the nanoindentation response, with consistent values achieved for a holding time of approximately 40 s. Phase-resolved nano-creep analysis further revealed that unreacted calcined kaolinite had the greatest indentation depth and lowest deformation resistance, whereas hydrated phases had higher stiffness and reduced creep compliance. Compared with OPC, LC3 showed greater viscosity and lower elasticity according to the BV model, which provided an excellent fit to the experimental data. The findings demonstrate that the time-dependent mechanical behavior of LC3 is primarily governed by the calcined clay portion. These findings highlight the potential use of LC3 for improving long-term deformation resistance and durability in sustainable cementitious systems.