When you fast, do not look somber as the hypocrites do, for they disfigure their faces to show others they are fasting. Truly I tell you, they have received their reward in full. But when you fast, put oil on your head and wash your face, so that it will not be obvious to others that you are fasting, but only to your Father, who is unseen; and your Father, who sees what is done in secret, will reward you. (Matthew 6:16-18 NIV)
The only fast that God actually required of the Jewish people was on the annual day of Atonement (Leviticus 23:27). The Pharisees fasted each Monday and Thursday (Luke 18:12) and did so in such a way that people knew they were fasting. Their purpose, of course, was to win the praise of men. As a result, the Pharisees lost God’s blessing.
It is not wrong to fast, if we do it in the right way and with the right motive. Jesus fasted (Matthew 4:3); so did the members of the early church (Acts 13:2). Fasting helps to discipline the appetites of the body (Luke 21:34) and keep our spiritual priorities straight. But fasting must never become an opportunity for temptation (1 Corinthians 7:7). Simply to deprive ourselves of a natural benefit (such as food or sleep) is not of itself fasting. We must devote ourselves to God and worship him. Unless there is devotion of the heart (see Zechariah 7), there is no lasting spiritual benefit.
As with giving and praying, true fasting must be done is secret; it is between the believer and God. To “make unsightly” our faces (by looking glum and asking for pity and praise) would be to destroy the very purpose of the fast. Our Lord here laid down a basic principle of spiritual living: Nothing that is truly spiritual will violate that which God has given us in nature. God usually does not tear down one good thing in order to build up another. If we have to look miserable to be considered spiritual, then there is something wrong with our views of spirituality.
(…exert from The Bible Exposition Commentary: Matthew-Galatians by Warren W. Wiersbe)