Background/Objectives: The glymphatic system plays a crucial role in clearing brain metabolic waste, and its dysfunction has been correlated to various neurological disorders. The Diffusion Tensor Imaging Analysis Along the Perivascular Space (DTI-ALPS) index has been proposed as a non-invasive marker of glymphatic function by measuring diffusivity along perivascular spaces; however, its sensitivity to sleep-related changes in glymphatic activity has not yet been validated. This study aimed to evaluate the feasibility of using the DTI-ALPS index as a quantitative marker of dynamic glymphatic activity during sleep. Methods: Diffusion tensor imaging (DTI) data were obtained from 12 healthy male participants (age = 24.44 ± 2.5 years; Pittsburgh Sleep Quality Index (PSQI) < 5), once while awake and 16 times during sleep, following 24 h sleep deprivation and administration of 10 mg zolpidem. Simultaneous MR-compatible electroencephalography was used to determine whether the subject was asleep or awake. DTI preprocessing included eddy current correction and tensor fitting. The DTI-ALPS index was calculated from nine regions of interest in projection and association areas aligned to standard space. The final analysis included nine participants (age = 24.56 ± 2.74 years; PSQI < 5) who maintained a continuous sleep state for 1 h without awakening. Results: Among nine ROI pairs, three showed significant increases in the DTI-ALPS index during sleep compared to wakefulness (Friedman test; p = 0.027, 0.029, 0.034). These ROIs showed changes at 14, 19, and 25 min after sleep induction, with FDR-corrected p-values of 0.024, 0.018, and 0.018, respectively. Conclusions: This study demonstrated a statistically significant increase in the DTI-ALPS index within 30 min after sleep induction through time-series DTI analysis during wakefulness and sleep, supporting its potential as a biomarker reflecting glymphatic activity.