As salam alaikum, I have a medicine that contains grain alcohol (ethanol) 60% by volume. I have to take 1 ml twice daily mixed in glass of juice or water. Is it permissible in Islam?
As long as you use alcohol for medical reasons and not for semiluxury food I don't see any qualms. The percentage of alcohol in your medicine is so low that it doesn't have any influence to your health.
Further, even Allah says that wine (Alcohol) has few benefits:
They ask you about wine and gambling. Say, "In them is great sin and [yet, some] benefit for people. But their sin is greater than their benefit." And they ask you what they should spend. Say, "The excess [beyond needs]." Thus Allah makes clear to you the verses [of revelation] that you might give thought. (2:219)
Briefly speaking, as a general Islamic rule, each sort of alcohol which is intoxicant, is counted as haram matters. But it seems has another ruling in the case of (medical) treatment. According to the ruling of Grand Ayatollah Khamenei:
… In the case that it is the alcohol which is intoxicant that basically is liquid, then it is considered as a haram matter and according to the precaution it is Najis as well. But taking it as a medicine in all cases doesn't matter. (The significant point is that seemingly you should do other permissible solutions, then refer to this matter, not…) http://www.ahkamekhamenei.blogfa.com/post/17/
Imam Khomeini has the similar view. In accordance with his ruling:
(medical)Treatment by every haram thing is permissible in the case that the treatment of a sick person is related to that. (Tahrir al Vasilah, Vol.2, Page176, M34) ((ترجمه تحریر الوسیله، ج2، ص176، م34))
On the other hand, it could be profitable for you to know in the case that the mentioned alcohol is related to ethanol, then it seems to be counted not as a haram sort of alcohol. Since it is related to the industrial alcohol which seems not to be haram. For further info. I recommend you to read the following site in regard to ethanol. http://www.islamquest.net/fa/archive/question/fa1309