From everything I have seen of Japanese military Yayoi period on-wards, there don't seem to be shields used really at all. Always made me curious, since I cant really see any parallels anywhere else.
They did actually use shields quite often during various periods of time depending on the necessities of that day and age. For example, according to Dorothy Perkins's book, The Samurai of Japan: A Chronology from their Origin in the Heian Era to the Modern Era, foot soldiers in eastern Japan were being equipped with shields and long spears during the sixth century.
However, a few hundred years later, they became embroiled in a war with the Emishi people who were primarily horsemen and would use their skills on the horse in hit and run attacks against the more infantry orientated Japanese forces. So, the Japanese forces adapted and began fielding horse archers of their own to combat that threat.
The samurai's armor adapted accordingly too to this threat. Since you can't use a bow without two hands, personal, hand-held shields became unviable so they instead latched those onto their armor. Large armor plates were attached to the shoulders to afford the guy extra protection in place of a personal shield. You can see a picture of that here.
Here's another painting of samurai combat where shields were heavily used.
And here's a drawing of Japanese musketeers shooting behind their shields.
I've talked about the prevalance of shields in Japanese warfare here. To extend upon /u/PapaJacky's response - not only are shields unwieldy on horseback alongside manipulating a bow, they simply didn't fit the style of battle that lasted throughout most of Japanese history. Spears and polearms also don't work too well with shields, which were the essential staple weaponry of Japanese armies.
hi, you'll find more in the FAQ section Ninjas, Samurai, and related errata:
Is it true that there were no shields in Japan during the Samurai and in that case why? - featuring /u/AsiaExpert
Why were shields so much more prevalent in warfare in Western Eurasia, Africa, and some parts of the Americas than in Chinese and Japanese warfare? - featuring /u/Abiding_Lebowski
also, this post may be of interest. Mostly it just links to the above, but it includes a few illustrations/photos
