The addition of background noise to an auditory signal delays brainstem response timing. This effect has been extensively documented using manual peak selection. Peak picking, however, is impractical for large-scale studies of spectrotemporally complex stimuli, and leaves open the question of whether noise-induced delays are frequency-dependent or occur across the frequency spectrum. Here we use an automated, objective method to examine phase shifts between auditory brainstem responses to a speech sound (/da/) presented with and without background noise. We predicted that shifts in neural response timing would also be reflected in frequency-specific phase shifts. Our results indicate that the addition of background noise causes phase shifts across the subcortical response spectrum (70–1000 Hz). However, this noise-induced delay is not uniform such that some frequency bands show greater shifts than others: low-frequency phase shifts (300–500 Hz) are largest during the response to the consonant-vowel formant transition (/d/), while high-frequency shifts (720–1000 Hz) predominate during the response to the steady-state vowel (/a/). Most importantly, phase shifts occurring in specific frequency bands correlate strongly with shifts in the latencies of the predominant peaks in the auditory brainstem response, while phase shifts in other frequency bands do not. This finding confirms the validity of phase shift detection as an objective measure of timing differences and reveals that this method detects noise-induced shifts in timing that may not be captured by traditional peak latency measurements.