Little is known about the neurophysiological correlates of lexical prosody in the comprehension of compound words, i.e., morphologically complex words. Here, it is investigated whether lexical prosody influences the decomposition of spoken compound words. In order to explore the neurophysiological correlates (event-related potentials, ERP) of a compound prosody, German native speakers had to judge the number agreement between numerals and nouns which did or did not agree in 50% of the cases. Importantly, the nouns carried either a compound or non-compound (single noun) prosody. The compound prosody led to increased reaction times (RTs) and reduced judgement accuracy. Critically, number violations for words with a compound prosody elicited an increased ERP negativity that was delayed by about 600 ms relative to a left-anterior negativity elicited by number violations for a single noun prosody. The ERP effect for the compound prosody preceded the according behavioural response by about 200 ms and the ERP peak latency effect correlated with the RT effect. These findings suggest that the ERP effect for the compound prosody could be functionally related to the accurate judgement performance for the compound prosody. The results suggest, more generally, that prosody plays a critical role in auditory compound comprehension and morphological processing.