If a person is unable to use water due to illness and water will harm him or her, it is permissible then to do tayammum to make taharah (ritual purification).
The late Shaykh Ibn Baz, a renowned Muslim scholar may Allah have mercy on him, said:
The Islamic Shari`ah is based on facilitation. Almighty Allah has made worship easier for those who are excused, according to their excuses, so that they will be able to worship Him without any hardship. Allah says:
(and [Allah] has not laid upon you in religion any hardship. ) (Al-Hajj 22:78)
(Allah intends for you ease, and He does not want to make things difficult for you.)(Al-Baqarah 2:185)
And the Prophet (peace and blessings be upon him) said: “When I command you to do a thing, do as much of it as you can.” And said, “Religion is easy.”
If a sick person is not able to purify himself with water, by doing wudu’ in the case of minor impurity or ghusl (bath) in the case of major impurity, because he is unable to do so or because he is afraid that it may make the sickness worse or delay his recovery, then he may do tayammum.
Tayammum is to strike both hands once on clean dust, then wiping the face with the insides of fingers and rubbing the hands together. Almighty Allah says,
(And if you are ill, or on a journey, or one of you comes after answering the call of nature, or you have been in contact with women (by sexual relations) and you find no water, perform Tayammum with clean earth and rub therewith your faces and hands (Tayammum).)(An-Nisa’ 4:43)
The one who is unable to use water comes under the same ruling as one who cannot find any water, because Allah says:
(So keep your duty to Allah and fear Him as much as you can.)(At-Taghabun, 64:16)
Also, the Prophet (peace and blessings be upon him) said: “When I command you to do a thing, do as much of it as you can.”