Perceptual benefits from digital noise reduction (NR) vary among individuals with different noise tolerance and sensitivity to distortions introduced in NR-processed speech; however, the physiological bases of the variance are understudied. Here, we developed objective measures of speech encoding in the ascending pathway as candidate measures of individual noise tolerance and sensitivity to NR-processed speech using the brainstem responses to speech syllable /da/. The speech-evoked brainstem response was found to be sensitive to the addition of noise and NR processing. The NR effects on the consonant and vowel portion of the responses were robustly quantified using response-to-response correlation metrics and spectral amplitude ratios, respectively. Further, the f0 amplitude ratios between conditions correlated with behavioral accuracy with NR. These findings suggest that investigating the NR effects on bottom-up speech encoding using brainstem measures is feasible and that individual subcortical encoding of NR-processed speech may relate to individual behavioral outcomes with NR.