It says so on the Wikipedia page for "Macrobiotic Diet," but it also says [citation needed.]
Asked on r/isitbullshit and was told to ask here as well.
In one word: no.
Japanese peasants mostly ate a diet consisting mostly of grains, with most of the rest coming from a variety of vegetables. Especially for those living near fishing areas, fish would have been included. Little meat would have been eaten (due to expense), and some might have avoided it altogether (for religious/social reasons).
There were periodic legal bans and restrictions on the killing of animals and the eating of meat. These were often based on religious reasons. Consider, e.g., from the Shurangama Sutra:
Both physically and mentally one must avoid the bodies and the by-products of living beings, by neither wearing them nor eating them.
Note that this also bans working with leather, wearing leather, handling meat, etc. Apart from the government, some shrines also issued regulations prescribing periods of uncleanliness after eating meat (up to 150 days for beef). The government also set times of uncleanliness for government officials and nobles who ate meat - this could be important since it could stop them from participating in ceremonies.
Many of the bans on killing and eating meat were only partial restrictions. For example, the oldest that we know of, Emperor Tenmu's ban of 675 prohibited the killing and eating of various animals (cattle, horses, dogs, chickens, monkeys) from April to September. Note that the ban only protected some animals, and only for part of the year. Hideyoshi's 1587 ban on beef-eating only protected cattle (and wasn't religiously motivated - it was to protect cattle for use as traction).
The strongest bans were in the Edo Period, notably under Tokugawa Tsunayoshi (the 5th Tokugawa shogun). In 1687, he banned the killing of animals and the eating of meat. He also passed a wide range of lifestyle-laws, banning prostitution, expensive fabrics, ordered people to protect abandoned children, give food to beggars, don't abandon your old families members, and a series of laws protecting dogs. (Many of these laws, taken together, are his famous "Edicts on Compassion for Living Things" (生類憐みの令), and were repealed almost immediately by his successor.) His first dog protection laws banned the killing of dogs (and causing them injury), which led to Edo's population of stray dogs growing very high. Tsunayoshi's next step was to have them housed and fed in government kennels.
The expense of meat meant that peasant consumption of meat was low. Social taboos (e.g., ritual uncleanliness) reduced meat consumption for all classes. Meat continued to be available, with some shops specialising in the sale of wild game. Rural villages had access to meat from hunting (permission to own guns was common for peasants, and hunting was one of the uses they could be put to). Even beef, which was the most restricted - dried sliced beef was sold during the Edo period, and beef was eaten by Tokugawa shoguns (beef pickled in sake was provided as a gift to the shoguns by the Hikone clan (who also produced dried beef - still available in Japan supposedly produced according to their traditional methods)).
It should be noted that there were ways around both laws and social taboos. One common method was to consume the meat as "medicine" (the Hikone clan's beef gifts to the shoguns were labelled as medicine).
This century, Japan's annual per capita meat consumption has varied about an average of about 70kg which, while lower than consumption in the USA, Australia, New Zealand, Canada, and most European countries, is much higher than it once was, having risen from under 10kg since 1962. (South Korea has shown a similar rise over the same time, from about 5kg to about 70kg.) While meat was available, most people in Japan during the Edo Period would have eaten most meals without meat.
The founder of the modern macrobiotic movement/diet, Nyoichi Sakurazawa (AKA George Ohsawa), was Japanese and his recommendations are based on the traditional Japanese diet. The vegetarian diet that he recommended (brown rice of other whole grains, vegetables, beans, miso) would cover most meals for many Japanese people before modernisation/Westernisation (noting that meals of mixed grains, e.g., rice and barley, rice and millet, etc., were usual). The non-vegetarian versions (including seafood) would cover most of the rest of their meals. But diets like this - grain-based, with vegetables as the main addition, and low in meat - were common for peasants in many parts of the work, and the low-meat component generally resulted from meat being too expensive rather than any legal restrictions on meat-eating.
(Some of this reply has been adapted from my earlier answers in https://www.reddit.com/r/AskHistorians/comments/asz87q/no_beef_eating_in_japan/ which includes references if you seek further reading on the evolution of the Japanese diet.)