What is the ruling on inhaling the smoke of some herbs for medicinal purposes?

Praise be to Allah.

The basic principle is that that which is harmful to the individual is prohibited, because Allah, may He be exalted, says:

{And do not kill yourselves} [An-Nisa’ 4:29]

{and do not throw [yourselves] with your [own] hands into destruction [by refraining]. And do good; indeed, Allah loves the doers of good} [Al-Baqarah 2:195].

The Prophet (blessings and peace of Allah be upon him) said: “There should be neither harming nor reciprocating harm.” Narrated by Ahmad and Ibn Majah (2341); classed as sahih by al-Albani in Sahih Ibn Majah.

If inhaling the smoke of these herbs is harmful, then it is haram to consume it.

If it is not harmful – rather it is of medicinal benefit, as you said – then there is nothing wrong with it, because the basic principle is that things are permissible.

You should consult specialists who have knowledge of the hoped-for benefit and can determine whether that can be achieved by burning these herbs or not.

And Allah knows best.