It's pretty much uncontroversial that, e.g., Liszt can be classified as Romantic, Bach as Baroque, Mozart mostly as Rococo (or Classical, if you must) and I'd argue that Debussy is an impressionist (possibly against Debussy's own opinion). Certainly, noone ever fits the shoes prefectly of any given genre, but there are certain major traits that make it fair to classify the artist under a genre. With that said:
Can Sergei Prokofiev be classified similarly in any music genre?
I can only classify him as producing Russian music of the 20th century... So, perhaps as a Russian and 20th century composer. Is there any better classification for him? He's one of my favorites, I'd like to find more music similar to his.