In most parts of Japan, except Hokkaido, June is known as a rainy month, called Tsuyu(梅雨）.
It normally begins from the beginning of June, and continues until the middle of July.
Unlike Malaysian rainy seasons, it sometimes rains all day, or it rains on and off all day long.
Visiting Japan during the tsuyu season?
If you are visiting Japan during the rainy season, I would recommend bringing an umbrella.
As the weather tends to be dreary and overcast, it is not suitable season for sightseeing, though you can still enjoy hot springs and indoor activities.
If you really want to avoid it, go to Hokkaido and enjoy its nicer weather.
Photo by Taicker(Creative Commons)