The King James Bible addresses fasting in several passages:
Matthew 6:16-18 (KJV)
16 Moreover when ye fast, be not, as the hypocrites, of a sad countenance: for they disfigure their faces, that they may appear unto men to fast. Verily I say unto you, They have their reward. 17 But thou, when thou fastest, anoint thine head, and wash thy face; 18 That thou appear not unto men to fast, but unto thy Father which is in secret: and thy Father, which seeth in secret, shall reward thee openly.
Isaiah 58:6-7 (KJV)
6 Is not this the fast that I have chosen? to loose the bands of wickedness, to undo the heavy burdens, and to let the oppressed go free, and that ye break every yoke? 7 Is it not to deal thy bread to the hungry, and that thou bring the poor that are cast out to thy house? when thou seest the naked, that thou cover him; and that thou hide not thyself from thine own flesh?
Joel 2:12 (KJV)
12 Therefore also now, saith the LORD, turn ye even to me with all your heart, and with fasting, and with weeping, and with mourning:
Acts 13:2-3 (KJV)
2 As they ministered to the Lord, and fasted, the Holy Ghost said, Separate me Barnabas and Saul for the work whereunto I have called them. 3 And when they had fasted and prayed, and laid their hands on them, they sent them away.
Matthew 17:21 (KJV)
21 Howbeit this kind goeth not out but by prayer and fasting.