All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
There is no harm on a person who is in a state of Ihraam to bathe in order to refresh or clean himself but he should be careful of what could cause the falling of his hair, or using something which contains perfume, like perfumed soap and the like, because applying perfume and cutting hair are amongst the prohibitions of Ihraam. Ibn Qudaamah said: 'There is no harm for a person in a state of Ihraam to gently wash his head and body, as 'Umar and his son did so, and 'Ali, Jaabir, Sa'eed Ibn Jubayr permitted it, as well as Ash-Shaafi'ee, Abu Thawr and other scholars." Moreover, Al-Bukhari reported that Abu Ayyoob Al-Ansaari washed his head while he was in a state of Ihraam and then said: "I saw the Prophet doing so [when he was in a state of Ihraam]".
For more benefit, please refer to Fataawa 86948 and 89172.
Allaah Knows best.