From the Wikipedia page 
In Japanese tradition, architectural spaces designed to be used for tea ceremony (chanoyu) gatherings are known as chashitsu (茶室, literally "tea rooms").
The term chashitsu came into use after the start of the Edo period (ca. 1600). In earlier times, various terms were used for spaces used for tea ceremony, such as chanoyu zashiki (茶湯座敷; "sitting room for chanoyu"), sukiya (place for poetically-inclined aesthetic pursuits [fūryū, 風流]) such as chanoyu), and kakoi (囲; lit., "partitioned-off space").
According to Japanese historian Moriya Takeshi in his article "The Mountain Dwelling Within the City," the ideal of wabi-style tea ceremony (wabi-cha) had its roots in the urban society of the Muromachi period (1336 to 1573), and took form in the tea houses that townspeople built at their residences and which affected the appearance of thatched huts in mountain villages. Before this, tea ceremony was generally enjoyed in rooms built in the shoin-zukuri architectural style, a style frequently employed in tea rooms built today.
Tea houses first appeared in the Sengoku period (mid-15th century to early 17th century), a time in which the central government had almost no practical power, the country was in chaos, and wars and uprisings were commonplace. Seeking to reclaim Japan, samurai were busy acquiring and defending territories, promoting trade and overseeing the output of farms, mills and mines as de-facto rulers, and many of the poor were eager to seek the salvation of the afterlife as taught by Zen Buddhism. Tea houses were built mostly by Zen monks or by daimyo, samurai, and merchants who practiced tea ceremony. They sought simplicity and tranquility - central tenets of Zen philosophy. The acknowledgment of simplicity and plainness, which is a central motivation of the tea house, continued to remain as a distinct Japanese tradition in the later periods.