Praise be to Allah.
It is permissible, after doing wudoo’, to dry the parts of the body washed in wudoo’, because the basic principle is that this action is permissible.
Ibn Qudaamah (may Allaah have mercy on him) said in al-Mughni (1/195): There is nothing wrong with drying the limbs with a towel after getting them wet during ghusl and wudoo’. This is what was narrated from Imam Ahmad. It was also narrated that ‘Uthmaan, al-Hasan ibn ‘Ali, Anas and many other scholars used a towel after doing wudoo’, and this is the more correct opinion, because the basic principle is that it is permissible. End quote.
Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) was asked about the ruling on drying the parts of the body that are washed in wudoo’
He replied: There is nothing wrong with drying them, because the basic principle is that it is not disallowed. The basic principle concerning anything other than acts of worship, such as contracts and actions, is that it is permissible and allowed, unless there is evidence that it is not allowed.
If someone were to say: How would you respond to the hadeeth of Maymoonah (may Allaah be pleased with her), where she says: The Prophet (peace and blessings of Allaah be upon him) did ghusl, and I brought the towel to him but he refused it and started to wipe the water with his hand?
The answer is that this action on the part of the Prophet (peace and blessings of Allaah be upon him) was a specific case which may be interpreted in several ways: either it was for a reason to do with the towel, or because it was not clean, or he did not want to wet it with the water because doing so was not appropriate. There are several possibilities, but the fact that she brought the towel to him indicates that it was his habit to dry himself, otherwise she would not have brought it to him. End quote.
Majmoo’ Fataawa Ibn ‘Uthaymeen (11/93).
And Allaah knows best.