Many people are reluctant to tell others that they are fasting so they will avoid the sin of the Pharisees: fasting just to gain recognition for themselves. I strongly believe that attitude is a result of a wrong interpretation of our Lord's teaching and that it is a trick of the enemy who does not want us to fast, nor to share with your loved ones, neighbors and friends the benefits of fasting.
By isolating ourselves from the support of other Christians, we will be more susceptible to doubts and negative influences (both human and demonic). We need the prayer shield of our Christian friends and family members to help us continue when we feel alone and when the enemy tempts us to give up Our Lord as he did Jesus Christ. Eventually, people will notice you are not eating.
However, I have found that unless you see them daily, they do not consider your skipped meal much of a concern. If you are asked, nonbelievers may be satisfied by such a brief answer as, “I have other plans for lunch today.” Or Christians should be satisfied when you answer that you are fasting today.
If friends and family express concern for your health, ease their fears by telling them that you will stop fasting the moment you feel you are harming your body or if the Lord leads you to end your fast. Tell them you are fasting under your doctor's care, which I urge you to do if you have any question concerning your health.
There is usually no reason for telling strangers or casual acquaintances that you are fasting. If you do, they may subject you to a lot of questions that you may not want to answer. But in any case, use your best judgment and the Lord's leading in telling people about your fast.