Fiqh-us-Sunnah Volume 4, Funerals and Dhikr, Fiqh 4.031.

The jurists are agreed on the permissibility of a wife washing the body of her dead husband. ‘Aishah said: “Had I known then what I know now, I would not have allowed anyone, except his wives, to wash the body of the Prophet.” This has been transmitted by Ahmad and Abu Daw’ud, and by al-Hakim, who considers it a sound hadith.

There is a difference of opinion, however, on the permissibility of the husband washing the body of his dead wife. The majority of scholars, nonetheless, consider it permissible, as is shown by a report, narrated by ad-Daraqutni and Al-Baihaqi, that Ali washed the body of Fatimah on her death. This is also supported by a hadith that the Prophet, peace be upon him, said to ‘Aishah: “If you die before me, I will myself wash you and enshroud you.” Ibn Majah records this hadith.

The Hanafi school holds that it is not permissible for a husband to wash his wife’s dead body, and if there is no other woman available then he should give her tayammum. However, the above hadith prove the contrary of this view.