It used to be a common practice for Lenten fasts.
There are different kinds of fasts. Extreme ones can be fatal.
We "break the fast" every day with breakfast. Intermittent fasting is a term that usually refers to just increasing the usual interval. Some fasts can completely abstain from food for weeks at a time (while maintaining salt and water). Other kinds of fasts are simply the act of fasting from a particular thing. Whether it is satiety, or meat, or something completely unrelated to food, what kind of fasting do you mean?
The intention of fasting mentioned in the Bible is usually about humility, and it's usually encouraged to be done privately instead of on open display for others.
"They rewarded me evil for good to the spoiling of my soul. But as for me, when they were sick, my clothing was sackcloth: I humbled my soul with fasting; and my prayer returned into mine own bosom." - Psalms 35:12-13 KJV
"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. But thou, when thou fastest, anoint thine head, and wash thy face; 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." - Matthew 6:16-18 KJV