Edmund, who was expected to play two singles rubbers, injured his back during practice in Birmingham.
His absence means Evans, 25, features in the GB team alongside Andy Murray, Jamie Murray and Dominic Inglot.
On Friday, Evans will play world number six Kei Nishikori, whom he beat in the first round of the 2013 US Open.
British number one Murray will kick off the tie against world number 87 Taro Daniel.
If Britain beat Japan they will face either Kazakhstan or world number one Novak Djokovic's Serbia.
