Groove, or the pleasurable urge to move to music, offers unique insight into the relationship between emotion and action. The predictive coding of music model posits that groove is linked to predictions of music formed over time, with stimuli of moderate complexity rated as most pleasurable and likely to engender movement. At the same time, listeners vary in the pleasure they derive from music listening: individuals with musical anhedonia report reduced pleasure during music listening despite no impairments in music perception and no general anhedonia. Little is known about musical anhedonics' subjective experience of groove. Here we examined the relationship between groove and music reward sensitivity. Participants (n = 287) heard drum-breaks that varied in perceived complexity, and rated each for pleasure and wanting to move. Musical anhedonics (n = 13) had significantly lower ratings compared to controls (n = 13) matched on music perception abilities and general anhedonia. However, both groups demonstrated the classic inverted-U relationship between ratings of pleasure & move and stimulus complexity, with ratings peaking for intermediately complex stimuli. Across our entire sample, pleasure ratings were most strongly related with music reward sensitivity for highly complex stimuli (i.e., there was an interaction between music reward sensitivity and stimulus complexity). Finally, the sensorimotor subscale of music reward was uniquely associated with move, but not pleasure, ratings above and beyond the five other dimensions of musical reward. Results highlight the multidimensional nature of reward sensitivity and suggest that pleasure and wanting to move are driven by overlapping but separable mechanisms.