Spoken language comprehension requires rapid and continuous integration of information, from lower-level acoustic to higher-level linguistic features. Much of this processing occurs in the cerebral cortex. Its neural activity exhibits, for instance, correlates of predictive processing, emerging at delays of a few 100 ms. However, the auditory pathways are also characterized by extensive feedback loops from higher-level cortical areas to lower-level ones as well as to subcortical structures. Early neural activity can therefore be influenced by higher-level cognitive processes, but it remains unclear whether such feedback contributes to linguistic processing. Here, we investigated early speech-evoked neural activity that emerges at the fundamental frequency. We analyzed EEG recordings obtained when subjects listened to a story read by a single speaker. We identified a response tracking the speaker’s fundamental frequency that occurred at a delay of 11 ms, while another response elicited by the high-frequency modulation of the envelope of higher harmonics exhibited a larger magnitude and longer latency of about 18 ms with an additional significant component at around 40 ms. Notably, while the earlier components of the response likely originate from the subcortical structures, the latter presumably involves contributions from cortical regions. Subsequently, we determined the magnitude of these early neural responses for each individual word in the story. We then quantified the context-independent frequency of each word and used a language model to compute context-dependent word surprisal and precision. The word surprisal represented how predictable a word is, given the previous context, and the word precision reflected the confidence about predicting the next word from the past context. We found that the word-level neural responses at the fundamental frequency were predominantly influenced by the acoustic features: the average fundamental frequency and its variability. Amongst the linguistic features, only context-independent word frequency showed a weak but significant modulation of the neural response to the high-frequency envelope modulation. Our results show that the early neural response at the fundamental frequency is already influenced by acoustic as well as linguistic information, suggesting top-down modulation of this neural response.