Does a rich husband have to sponsor his wife’s Hajj?

The husband is not Islamically obliged to pay for his wife’s Hajj, even if he is rich, rather that comes under the heading of kind treatment, and she is not obliged to do Hajj because she cannot afford it. 

And Allah is the Source of strength. May Allah send blessings and peace upon our Prophet Muhammad and his family and companions. End quote. 

Standing Committee for Academic Research and Issuing Fatwas 

Shaykh ‘Abd al-‘Azeez ibn ‘Abd-Allah ibn Baaz, Shaykh ‘Abd al-Razzaaq ‘Afeefi, Shaykh ‘Abd-Allah ibn Qa’ood. 

Fatawa al-Lajnah al-Daa’imah li’l-Buhooth al-‘Ilmiyyah wa’l-Ifta (11/35). 

It also says in Fatawa al-Lajnah al-Daa’imah (11/94): 

The husband is not obliged to pay for his wife’s Hajj as he is obliged to pay for her food, clothing and shelter, but doing so comes under the heading of kind treatment and good manners, and she is entitled to the same maintenance when travelling for Hajj as she is when staying at home. End quote. 

Shaykh ‘Abd al-‘Azeez ibn ‘Abd-Allah ibn Baaz, Shaykh ‘Abd al-Razzaaq ‘Afeefi, Shaykh ‘Abd-Allah ibn Qa’ood.