The temporal structure of sound such as in music and speech increases the efficiency of auditory processing by providing listeners with a predictable context. Musical meter is a good example of a sound structure that is temporally organized in a hierarchical manner, with recent studies showing that meter optimizes neural processing, particularly for sounds located at a higher metrical position or strong beat. Whereas enhanced cortical auditory processing at times of high metric strength has been studied, there is to date no direct evidence showing metrical modulation of subcortical processing. In this work, we examined the effect of meter on the subcortical encoding of sounds by measuring human auditory frequency-following responses to speech presented at four different metrical positions. Results show that neural encoding of the fundamental frequency of the vowel was enhanced at the strong beat, and also that the neural consistency of the vowel was the highest at the strong beat. When comparing musicians to non-musicians, musicians were found, at the strong beat, to selectively enhance the behaviorally relevant component of the speech sound, namely the formant frequency of the transient part. Our findings indicate that the meter of sound influences subcortical processing, and this metrical modulation differs depending on musical expertise.