The time-dependent plastic deformation response of magnesium/carbon nanotube (CNT) nanocomposites containing 0.25, 0.5, and 0.75 vol% of carbon nanotubes is investigated through depth nanoindentation tests against monolithic pure magnesium in the present study. The Mg-CNT nanocomposite materials were successfully synthesized via a powder metallurgy technique coupled with microwave sintering followed by hot extrusion to produce 8-mm diameter, long solid bars. All depth-sensing indentation creep tests were conducted at ambient (room) temperature employing a diamond Berkovich pyramidal indenter. These tests are dual-stage, i.e., loading to a prescribed peak load of 50 mN, holding the peak load constant for a dwell period of 500 s, and finally unloading. Various strain rates of 0.01, 0.1, 1, and 10 s−1 were performed to assess the effects of strain rate and dwell time on the ambient temperature creep response of the Mg-CNT nanocomposites. The outcomes of these tests are explained through material hardness, microstructure, the extent of CNT content in each material, and strain rate sensitivity. Upon analyzing the nanoindentation creep tests, the dominant creep mechanism at room temperature was found to be a dislocation creep mechanism. It is also found that CNTs increase the creep resistance of magnesium. Findings of this study can be used as a starting point for a high-temperature creep study on Mg-CNT nanocomposites. This paper is a continued study from our group on time-dependent plastic deformation of Mg nanocomposites (i.e., see Haghshenas et al., Journal of Composite Materials, https://doi.org/10.1177/0021998318808358 ). The short-term goal is to provide a compressive picture of the controlling creep mechanisms and their dependency upon, time, temperature, strain rate, volume fraction of the nanoparticles, and the type of the nanoparticles. Mg, in general, is a notorious material for high-temperature application; therefore, the long-term objective is to propose Mg nanocomposite as reliable replacements for Mg when lightweight and creep resistance are needed. However, to be able to confidently suggest such a replacement detailed understanding on the controlling phenomena, mention as short-term goals, are required.