Should juveniles be institutionalized for using drugs?

Disadvantages
One of the problems with being incarcerated or institutionalized for drug use is that juveniles miss curriculum/instruction time in schools. It's hard enough for students who attend school regularly to meet curricular requirements, so being incarcerated for drug use may place these juveniles at a direct disadvantage do to time missed. This further creates a gap in personal development, gap in academic success, socialization/communication skills being undeveloped and being unemployable short-term do to arrest records (depending on the local). One could further argue a positive correlation with students who are on "paper," or being adjudicated through local/state juvenile justice systems, and not finishing secondary requirements all together. This may further place these juveniles behind the success curve and might add to prison recidivism, becoming a burden on tax payers.
Advantages
Not all illegal substances have the same affect on juveniles, so some behavior may be considered more risk adverse do to what is consumed. Example: Marijuana and alcohol are widely proven damaging to a developing young person, but bath salts or spice can cause severe brain damage to a juvenile immediately through one use. Incarceration may be morally and ethically justified if it means saving a young persons life.

To start, there are multiple criteria that need to be examined to decide such a thing as this question is obviously vastly multifaceted.
One of the most prevalent, but not necessarily the most important criteria is age. More specifically level of maturity. Certainly a young child can be very mature, but I wouldn't say that a young child could be mature enough to use drugs, so it seems there is some sort of cut off point where maturity seems to matter less and age more. It is difficult to say where this cut off point is especially due to its subjectivity. Now, if a child can be classified as too young to be using drugs it may be counterproductive to institutionalize them apart from a short hospital visit. I think intervention is definitely necessary, but not to the extreme of complete institutionalization, whatever that may mean.
Another important set of criteria is the frequency of use, and which drug(s) is/are being used. I think the severity of the damage the drug is doing, coupled with the level of frequency can be used to determine whether institutionalization is necessarily in most cases. What institutionalization means should be determined on a case by case basis, and choosing something too intense can, again, be counterproductive. It is difficult to say what level of frequency is a problem. Severity of damage may be easier to judge.
Now to what seems to be the root of the question. Is it ethical? Well, I think it can be in scenarios when there seems to be no other way to help a child. This is tricky because, as I mentioned earlier, the severity of the treatment must be carefully chosen in line with the severity of the substance use. I think institutionalization generally has a connotation of intensity and in the lock-down, so to speak, sense of the word I think there are many ways that could render it unethical. On the other side of the definition, institutionalization meaning any form of residential treatment can be completely ethical so long as the stay is not prolonged unnecessarily and is the right fit for the child.
My personal opinion is that some other things should be tried prior to residential treatment/institutionalization as these things have a profound effect on children. It may seem like the only option at times and if it is, then it is, but a gentler approach can sometimes be more effective.

This is a tough question and a great one to debate. The first thing to point out is that "institutionalized" doesn't necessarily mean prison. It could mean a juvenile detention center or a hospital.
I would argue that each case should be argued on merit. For example, if a ten-year-old is found smoking marijuana, prison is certainly not the place for him. In a case like this, I would recommend the intervention of social services and probably counseling.
On the other hand, a seventeen-year-old who is a regular cocaine user probably needs to go to a rehab center. In my way of thinking, this is still not justification for imprisonment, because he has harmed only himself. Given that cocaine is a highly addictive and destructive substance, he would need to spend time at a rehab facility.
The scenario changes drastically if that seventeen-year-old is dealing cocaine. Being a drug dealer means that you are causing untold harm to other individuals and families by making drugs ready available. A seventeen-year-old who is dealing should do time in a juvenile detention center.