Is it permissible to take medicine that is made from the roots of a tree and was boiled in wine?

It is not permissible to make medicine in this manner,
because it involves using wine or alcohol, and Allah has commanded us to
avoid alcohol, as He says (interpretation of the meaning):

“So avoid (strictly all) that (abomination) in order that
you may be successful”

[al-Maa’idah 5:90].

And the Prophet (blessings and peace of Allah be upon him)
forbade making medicine from wine and he said that wine is a disease and is
not a remedy. 

Muslim (1984) narrated that Taariq ibn Suwayd al-Ju‘fi (may
Allah be pleased with him) asked the Prophet (blessings and peace of Allah
be upon him) about wine and he forbade him or expressed his disapproval of
his making it. He said: I only make it as a remedy. He said: “It is not a
remedy; rather it is a disease.” 

An-Nawawi (may Allah have mercy on him) said: 

This indicates that it is haraam to store alcohol [i.e., to
keep it] and to make it into vinegar, and it is a clear statement that it is
not a remedy and it is haraam to use it for medicinal purposes.

End quote. 

For more information, please see the answer to question no.
41760 

But… If the medicine has been manufactured in this haraam
manner, it is permissible to use it if the alcohol has been absorbed into
this medicine and there is no trace of it left in the form of colour, taste
or smell. 

But if there is still some trace of it in the medicine, it is
not permissible to use it, because using it constitutes using and consuming
alcohol. 

Al-Bahooti (may Allah have mercy on him) said: 

If the intoxicant is mixed with water and is absorbed into it
then he drinks it, the hadd punishment is not to be carried out on him,
because by being absorbed into the water, it did not change the nature of
the water. 

End quote from Kashshaaf al-Qinaa‘, 6/118 

Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him)
said: 

If alcohol falls into water and is absorbed, then someone
drinks it, he is not drinking alcohol and he does not have to be given the
hadd punishment for drinking alcohol, if nothing of its taste, colour or
smell remained. If a woman’s milk is poured into water and is absorbed to
the extent that no trace of it is left, and a child drinks that water, he
does not become her son through breastfeeding thereby.

End quote from Majmoo‘ al-Fataawa, 21/33 

The scholars of the Standing Committee for Issuing Fatwas
said: 

It is not permissible to mix medicines with alcohol, but if
it has been mixed with alcohol it is permissible to use it if the ratio of
alcohol is low and its traces do not appear in the colour, taste or smell of
the medicine. Otherwise it is haraam to use anything that has been mixed
with it. 

End quote from Fataawa al-Lajnah ad-Daa’imah, 25/39 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: 

Alcohol is an intoxicating substance as is well known, so it
is khamr, because the Prophet (blessings and peace of Allah be upon him)
said: “Every intoxicant is haraam,” and according to one report he said,
“Every intoxicant is khamr.” 

Based on that, if this alcohol is mixed with something and
was not absorbed into the substance it was mixed with, then this mixture
becomes haraam, because this mixture still has a trace of alcohol. But if
this alcohol has been absorbed into what it is mixed with and no trace of it
appears, then it is not haraam. 

End quote from Fataawa Noor ‘ala ad-Darb, 122/21 

He also said: 

With regard to the mixing of some medicines with a small
amount of alcohol, that does not necessarily mean that they are haraam, if
the alcohol in the mixture is very little and no trace of it remains with
what it has been mixed with.

End quote from Majmoo‘ Fataawa wa Rasaa’il Ibn ‘Uthaymeen,
11/193 

And Allah knows best.