Having read the accounts from many of the diaries of Japanese and Chinese Sailors sent as emissaries or envoys to the west for exploratory and diplomatic reasons (Decent sources to answer your question as most of them describe the foods they were given by foreigners when they eventually met with Western Peoples and thus obviously compare it to the food they had been eating on their journey, while usually a Sailor would have less cause to describe their daily diet in any great detail, they always talk about what they've been eating on their journey whenever they need to compare and contrast western food to their own cuisine) it should come as no great surprise that the answer is Rice and Rice Wine.

For Japanese Sailors in particular It would seem that the primary source of Protein was fish and the fish were acquired on their voyage and often the rice was just eaten on its own there is no description I personally saw of meat or fish or really much of anything other than Rice being taken with them for the voyage. Individual Sailors seemed to have their own personal bottles of Sauce or Spices or whatever means of flavouring their rice they preferred, it does not seem that the ships rice cook would make a large batch of sauce or flavouring to go with the rice for everyone, but just dole out the crew a bowl of rice each and they would season or flavour it themselves.

Over the centuries, many voyages went to the west and thus many Sailors talked about their food in comparison to the banquets or offerings their hosts gave them. An example of a very well explained and documented Voyage was the Iwakura Mission, a diplomatic mission between Europe the US and Japan during the Meiji Period conducted between 1871-1873. It has been translated into English and can be found Here Another decently documented voyage of a similar nature was made by Hasekura Tsunenaga from 1613 to 1620. Called the Keicho Embassy.

This is only the most extensively detailed (and unlikely to be sensationalised or falsified, not all of the claims such travellers make can be verified or seems very believable, some probably are stretching or fabricating the truth) report I can recall of course, we can read reports of such missions throughout history, with people sailing to attempt to make contact with the West as far back as Han travellers heading along the Arabian Sea trying to travel to Rome for example.

The Logistical Reports for the Ming Dynasty Navy rarely made mention of anything other than Rice, Millet, Salt and Vinegar being doled out to their Sailors, Fresh Meat or Vegetables were anecdotally seen as rare treats whenever they could get their hands on them, but clearly they were never distributed on any such scale as to appear in the bereaucratic records of the supply chain, but there was decent use of Pickled and Fermented or Cured Meat, Fish and Vegetables and even Fermented Bread (Although this was used as an addition to meals rather than as a food, being broken up and the crumbs added to the dish, think like how Croutons are used in a Salad). It being the Ming Dynasty of course there was also Tea available, dried and moulded into bricks.

Sun, or Sun Fan was commonly used, which. although prepared in a different way, was basically exactly the same thing as modern Instant Rice, pre cooked rice that stores incredibly well and can be eaten quickly simply by pouring hot water over it. Two "Dou" of Sun Fan was rationed to each sailor for fifty days worth of meals.

Vinegar was transported not bottled as storing liquids was incredibly difficult and expensive, but instead by steeping a cloth in the Vinegar and allowing it to dry, a small piece of the Vinegar soaked cloth would be cut out and added to the food while cooking, the Vinegar seeping out as the Cloth burned away. One strip of cloth was rationed to each sailor for fifty days worth of meals.