The Messenger (blessings and peace of Allah be upon him) instructed us to wash the traces of madhiy from the penis. In some hadiths it mentions washing the testicles too.
It was narrated that ‘Ali said: I was a man who emitted a great deal of madhiy (prostatic fluid), so I asked a man to ask the Prophet (blessings and peace of Allah be upon him) about that because I was too shy to ask him because of being married to his daughter, and he said: “Do wudoo’ and wash your private part.”
Narrated by al-Bukhaari (269) and Muslim (303).
See also fatwa no. 175125
Ibn Hajar (may Allah have mercy on him) said:
This indicates that madhiy is najis (impure), as is apparent.
End quote from Fath al-Baari (1/381)
Ibn ‘Abd al-Barr (may Allah have mercy on him) even stated that there was no difference of opinion concerning this matter, as he said:
The scholars did not differ concerning the fact that anything that is emitted from the penis, other than maniy (semen), is najis.
End quote from al-Istidhkaar (3/111)
As it is established that it is najis, and there is the command to wash it from the private part, it should also be washed from the remainder of the body, like any other impure substance. Otherwise, Islamic rulings are lenient with regard to purifying one’s garment of it, so it is sufficient to sprinkle water on the place that the madhiy got on to, and there is no instruction to wash it.
What is expected of the Muslim with regard to shar‘i commands is that he should do as much of them as he can. Allah, may He be exalted, says (interpretation of the meaning):
“So keep your duty to Allah and fear Him as much as you can”
So if a person has a continual emission of madhiy, and he is not able to prevent it from coming out, but he is able to prevent it spreading, then when he does wudoo’ for prayer, he must use something to prevent it spreading, such as wrapping some cloth or tissue around the head of the penis, and the like, then he may pray.
Ibn Qudaamah (may Allah have mercy on him) said:
The woman who is suffering from istihaadah (irregular, non-menstrual bleeding), one who is suffering from incontinence or continual emission of madhiy, or a wound that does not stop bleeding, and others in similar situations in which minor impurity is ongoing and the individual is not able to maintain a state of purity (tahaarah), must do wudoo’ for each prayer, after washing the site of the impurity, then wrapping it and taking precautions to prevent the impurity spreading, by whatever means he or she is able to.
So the woman who is suffering from istihaadah should wash the site of the bleeding, then wrap it with cotton and the like, to block the blood (and prevent it from spreading), because the Prophet (blessings and peace of Allah be upon him) said to Hamnah, when she complained to him of excessive bleeding: “I suggest you use a piece of cotton, for it will absorb the blood.” If the blood cannot be absorbed by a piece of cotton, then she may use a piece of cloth which she should tie around herself, covering the private part. This is what is mentioned in the hadith of Umm Salamah: “Tie a cloth around yourself” and he (the Prophet – blessings and peace of Allah be upon him) said to Hamnah: “Tie something around yourself,” when she said: It is more than that.
The same applies to one who is suffering from incontinence or continual emission of madhiy. He should put a piece of cloth over the end of the penis and take whatever precautions he can, and do what we have mentioned above.
End quote from al-Mughni (1/421-422)
If you find it too difficult to wrap something over your penis, then you can do that only at the time of doing wudoo’, until you have finished praying, then you can remove that protection, and after that you can simply put a piece of cloth, tissue and the like, between your penis and your underwear, so that you will not become najis, and so that when you do wudoo’ and offer the following prayer, you will only have to change this piece of cloth, instead of changing or washing your clothes.
It is not permissible for you to pray in a garment that is najis (impure) or that has madhiy on it, until you have purified it.
And Allah knows best.