The Holy Qur'an speaks about "fasting" in no less than 4 different places

1.In Surah AL-BAQARA chapter number 2 verse number 183
"O you who believe! fasting is prescribed for you, as it was prescribed for those before you, so that you may guard (against evil). "

2.In Surah AL-BAQARA chapter number 2 verse number 196
"And accomplish the pilgrimage and the visit for Allah, but if, you are prevented, (send) whatever offering is easy to obtain, and do not shave your heads until the offering reaches its destination; but whoever among you is sick or has an ailment of the head, he (should effect) a compensation by fasting or alms or sacrificing, then when you are secure, whoever profits by combining the visit with the pilgrimage (should take) what offering is easy to obtain; but he who cannot find (any offering) should fast for three days during the pilgrimage and for seven days when you return; these (make) ten (days) complete; this is for him whose family is not present in the Sacred Mosque, and be careful (of your duty) to Allah, and know that Allah is severe in requiting (evil). "

3.In Surah AL-MAEDA chapter number 5 verse number 89
"Allah does not call you to account for what is vain in your oaths, but He calls you to account for the making of deliberate oaths; so its expiation is the feeding of ten poor men out of the middling (food) you feed your families with, or their clothing, or the freeing of a neck; but whosoever cannot find (means) then fasting for three days; this is the expiation of your oaths when you swear; and guard your oaths. Thus does Allah make clear to you His communications, that you may be Fateful. "

4.In Surah AL-MAEDA chapter number 5 verse number 95
"O you who believe! do not kill game while you are on pilgrimage, and whoever among you shall kill it intentionally, the compensation (of it) is the like of what he killed, from the cattle, as two just persons among you shall judge, as an offering to be brought to the Kaaba or the expiation (of it) is the feeding of the poor or the equivalent of it in fasting, that he may taste the unwholesome result of his deed; Allah has pardoned what is gone by; and whoever returns (to it), Allah will inflict retribution on him; and Allah is Mighty, Lord of Retribution."

 For more on The Holy Qur'an visit Dr. Zakir Naik's site.