The first music video-like would be The Little Lost Child in 1894 (!!). This is considered more like the first illustrated song. Using a magic lantern, a series of still images were projected on a screen simultaneous to live performances.
Also, Silly Symphony (1929-39) and Fantasia (1940) were animated films/videos (the former one short) that were structured around music. Thus, technically they are music videos.
The first music video as we know it today, was Tony Berrett's Stranger in Paradise(1953) (cannot find it online).
The next music video was Elvis's Jailhouse Rock (1957)