Evidence is accumulating that similar cognitive resources are engaged to process syntactic structure in music and language. Congenital amusia – a neurodevelopmental disorder that primarily affects music perception, including musical syntax – provides a special opportunity to understand the nature of this overlap. Using electroencephalography (EEG), we investigated whether individuals with congenital amusia have parallel deficits in processing language syntax in comparison to control participants. Twelve amusic participants (eight females) and 12 control participants (eight females) were presented melodies in one session, and spoken sentences in another session, both of which had syntactic-congruent and -incongruent stimuli. They were asked to complete a music-related and a language-related task that were irrelevant to the syntactic incongruities. Our results show that amusic participants exhibit impairments in the early stages of both music- and language-syntactic processing. Specifically, we found that two event-related potential (ERP) components – namely Early Right Anterior Negativity (ERAN) and Left Anterior Negativity (LAN), associated with music- and language-syntactic processing respectively, were absent in the amusia group. However, at later processing stages, amusics showed similar brain responses as controls to syntactic incongruities in both music and language. This was reflected in a normal N5 in response to melodies and a normal P600 to spoken sentences. Notably, amusics’ parallel music- and language-syntactic impairments were not accompanied by deficits in semantic processing (indexed by normal N400 in response to semantic incongruities). Together, our findings provide further evidence for shared music and language syntactic processing, particularly at early stages of processing.