I don't know why it is so uncommon in literature, however the solution suggested by gung (projecting your pairwise distances into a Euclidean space using Principal Coordinates Analysis, for example through this package if you use R) is simple and doesn't require specialized algorithms. I personally used it here embedded in an optimization framework and it worked fairly well.

I don't know why it is so uncommon in literature, however the solution suggested by @gung and @ttnphns (first projecting your pairwise distances into a Euclidean space using Principal Coordinates Analysis, for example through this package if you use R, and then doing K-means usual way) is simple and doesn't require specialized algorithms. I personally used it here embedded in an optimization framework and it worked fairly well.