The iOS Music app now shows a Music Videos section when you browse Apple Music.
This shows featured videos at the top of the page, followed by New Music Videos, Music Video Playlists, then some sections by genre and one for the “Essential ’80s.” There are only three genres for now – hip-hop, pop, and rock – though that probably covers the majority of music videos available in the west. (Bollywood videos are certainly a big thing in India.)
This is another step toward Apple Music becoming more than just a music service, but expanding to what will eventually become a full range of video content. You can check one out here.
This section does not yet appear in iTunes on the desktop, but should show up soon.
Update: the Music Videos section now shows in iTunes as well.