Is the observed link between musical ability and non-native speech-sound processing due to enhanced sensitivity to acoustic features underlying both musical and linguistic processing? To address this question, native English speakers (N = 118) discriminated Norwegian tonal contrasts and Norwegian vowels. Short tones differing in temporal, pitch, and spectral characteristics were used to measure sensitivity to the various acoustic features implicated in musical and speech processing. Musical ability was measured using Gordon's Advanced Measures of Musical Audiation. Results showed that sensitivity to specific acoustic features played a role in non-native speech-sound processing: Controlling for non-verbal intelligence, prior foreign language-learning experience, and sex, sensitivity to pitch and spectral information partially mediated the link between musical ability and discrimination of non-native vowels and lexical tones. The findings suggest that while sensitivity to certain acoustic features partially mediates the relationship between musical ability and non-native speech-sound processing, complex tests of musical ability also tap into other shared mechanisms.