To precisely measure radon concentrations in purified air supplied to the Super-Kamiokande detector as a buffer gas, we have developed a highly sensitive radon detector with an intrinsic background as low as 0.33$pm$0.07 mBq/m$^{3}$. In this article, we discuss the construction and calibration of this detector as well as results of its application to the measurement and monitoring of the buffer gas layer above Super-Kamiokande. In March 2013, the chilled activated charcoal system used to remove radon in the input buffer gas was upgraded. After this improvement, a dramatic reduction in the radon concentration of the supply gas down to 0.08 $pm$ 0.07 mBq/m$^{3}$. Additionally, the Rn concentration of the in-situ buffer gas has been measured 28.8$pm$1.7 mBq/m$^{3}$ using the new radon detector. Based on these measurements we have determined that the dominant source of Rn in the buffer gas arises from contamination from the Super-Kamiokande tank itself.
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