It's hard to make specific recommendations without knowing what kinds of books you typically enjoy. That is, if you want "more like Murakami," that's one thing, but if you want "Japanese authors who write about things I normally enjoy," that's another. If you could explain what you enjoy, that would help us recommend more. :)

As a general shotgun approach at "who's who" in Japanese literature:

Kobo Abe's Woman in the Dunes is a story that's a bit bizarre/unreal; many people I know who like Murakami also like this.

Speaking of "bizarre," Yukio Mishima was quite a character -- aside from that, he was also quite a writer. Patriotism is a great short story from him that's pretty thought-provoking in a lot of ways.

Mishima's Confessions of a Mask is also another book I'd immediately recommend to people looking at Japanese literature. The protagonist is homosexual and somewhat deviant in a number of ways; the book looks at what it means to be "abnormal" and still have to fit into Japanese society (IIRC this was set in pre-war Imperial Japan).

For more modern stuff, Taiyo Fujii's Gene Mapper was a great read and a look at a future where genetic engineering/manipulation is the norm, especially for foodstuffs.