It is not permissible to fast during the three days following the ‘Id al-Azha. Abu Hurairah reported that the Messenger of Allah, upon whom be peace, sent ‘Abdullah ibn Huzhaqah to announce at Mina: “You are not to fast these days. They are days of eating and drinking and remembering Allah.” This is related by Ahmad with a good chain.
Ibn ‘Abbas reported that the Messenger of Allah, upon whom be peace, sent a person to announce: “Do not fast on these days, as they are days of eating, drinking and rejoicing with one’s family.” At-Tabarani related it in al-‘Awsat.
The Shaf’iyyah allow fasting on the days of tashreeq if there is some reason for the fasting – that is, if it is due to an oath, for expiation, or for making up a missed day of Ramadan. Those fasts that have no special reason behind them are not allowed, and there is no disagreement on this point. The Shaf’iyyah applied the same reasoning that they used in saying that prayers that are performed for a specific reason are allowed to be performed during the prohibited times of prayer [for example, the prayer of salutation to the mosque, and so on].