The short answer is no.
But a surprising number of otherwise well-educated Japanese people believe this. The argument is usually presented as something along the lines of "The Japanese were traditionally agricultural people. Our ancestors didn't eat much meat, so we evolved a longer intestine to digest grains and vegetables." The idea is usually presented as a contrast to Westerners, especially Americans, who are said to eat much more meat. It is also sometimes used as part of an argument that Japanese should eat less meat. In general, the Japanese intestine is said to be one metre longer than other intestines, or even 1.5 times longer.
Well, where to begin with such a claim? There seems to be little definitive information available on racial differences in intestinal length on the net, though plenty of people have been asking the question. There used to be a wikipedia article, but it was deleted, seemingly because of lack of evidence. The belief is certainly a prime example of nihonjinron, the theory that Japanese are in some way unique, and by implication superior, in various cultural, physical and mental characteristics.
It seems (to me anyway) to imply that people in other countries are more carnivorous, and by extension more aggressive or violent. It was famously presented as a given fact by the Japanese minister for agriculture in Tsutomu Hata in 1987 when arguing against American beef imports. Although in the resulting furore he lost his job, he was possibly only repeating what most Japanese perceive as common wisdom. Around the same time it was claimed that Japanese snow was different, which was used to justify slapping a tariff on imported French skiis.
The theory that Japanse intestines are longer as an adaption to eating more grain and less meat seems superficially plausible. Westerners do, in fact, eat more meat than Japanese, who even today tend to have a diet rich in seafood and vegetables. However, the theory is actually specious and pretty easily dismissed.
For one thing, the adaption aspect of this is decidedly dodgy. Although human evolution has continued since the invention of agriculture (for example the spread of lactose tolerance through European populations), the lengthening of the human gut by a metre or more seems to be quite a stretch (as it were). Gut tissue is metabolically expensive. An extra meter of it would require considerable resources, and some other body organ would suffer to provide the space. Even if this were possible, it would imply massive selection pressure. Actually it is theorized by some evolutionary scientists that reduction of the gut associated with increased meat consumption may have allowed early evolving humans to devote greater metabolic energy to brain growth and maintenance, thus preciptating 'a great mental leap forward'. This is known as the "expensive tissue hypothesis". Funnily enough, no Japanese person has ever suggested to me that their intestinal lengthening may have been accompanied by brain size reduction. You probably won't find many references to brain shrinking in popular Nihonjinron books and articles.
Secondly, it is not as if the Japanese diet was really that peculiar. Sure, recently American or European populations have been eating more meat, but go back a few hundred years and common people in agricultural societies all over the world were subsisting on grains, vegetables, and much smaller amounts of protein. Meat, in Japan and elsewhere, was reserved for the nobility. This idea of Japanese 'uniqueness' just doesn't stand up to close scrutiny.
Going back further, none of the various human populations in the world are especially suited to to eating a large percentage of their diet in grain form. Hunter gatherers didn't. Indeed, if you follow the Japanese reasoning to its conclusion, the Egyptians and Sumerians (now Iraqis) should have the longest intestines in the world, since they live where grain domestication started. Indeed, farming didn't come to Japan until substantially later, in about 300 BC with the Yayoi people, several centuries after the Golden Age of Ancient Greece and some 5000 years or so after domestication of the first grains in the Fertile Crescent.
All this is not to say, strangely enough, that many individual Japanese do not actually have longer intestines than Westerners. There seems to be some evidence that intestinal length may depend on an individual's diet in their lifetime, with longer intestines associated with less meat consumption. However this would be a cultural phenomenon, not a racial.
The issue is kind of frustrating because it seems like the kind of thing which should be easily testable. However it could be quite difficult research to do. Living or dead people? How do you exclude cultural factors such as diet and body size? Who do you include or exclude? Do you exclude Chinese or Koreans from the long intestine sample? If so, why? What is the standard variation in normal intestine length? How many individual guts do you need to measure to arrive at a statistically valid conclusion?
In the absence of definitive medical evidence, I would hesitate to say that the Japanese are definitely wrong about this. But it seems very likely to me that they are, and certainly a case where an extraordinary claim requires extraordinary evidence.