A beautiful writer, albeit more British than Japanese, is Kazuo Ishiguro.
His masterful character-studies are completely involving. Whether the story is seen through the eyes of a butler (Remains of the Day), or a human Guinea pig (Never Let Me Go), the proceedings are flawlessly executed.
Ishiguro isn't called a modern master for nothing. These books read like Dickensian classics set in recent times, and deserve every award they've won.
The outlook and style is very mature and often heavy-going, but the vividness of the characters is second to none, and totally inescapable.
Over the years Ishiguro has written disappointingly few books, but I urge you to read them all asap. There are also a couple of movie adaptations. Results have been mixed, but Anthony Hopkins' performance in Remains of the Day (also one of the best books) is still a classic.
I'd also recommend An Artist of the Floating World; something of a retrospective on Japan during WWII.
If you're thinking of buying any of Ishiguro's books, then please help us out by doing so through Amazon (all earnings go to Tohoku victim support):
Contemporary Writers page about Ishiguro.