Short answer is you can't. Longer version goes like this...
Even if you have a perfect definition of an ethnic group, and that's what you mean by minority group, you can't guarantee that your genetically engineered virus is going to ONLY attack people of that ethnicity, and that it's going to attack EVERYONE of that ethnicity; biology and genetics has proven consistently over time that things just don't work that way. Let's however look at some of the reasons why;
1) Natural Resistance
The existence of things like MRSA (multi-resistant Staph-Aureus, or resistant Golden Staph) is an example of how by wiping out a massive number of a specific group, all you're really doing is filtering out those who are susceptible to your attacks. MRSA is effectively a super-bug that infects people while at the same time being resistant to almost all anti-biotics, meaning that there's no remaining effective treatment for people who become infected with this bug. Worse, we pretty much created it by wiping out its weaker strains through the mass application of anti-biotics. There is no disease that will ever be 100% effective in wiping out a particular species, race or even bacteria. The trouble is that when we try, we create a stronger species, race or bacteria insofar as the only options for reproduction among the survivors are those who are also resistant.
2) Complexity of DNA
The problem you have is that given that DNA represents a MASSIVE number of atoms (around 8.5 billion according to one estimate), the sequence that you want to target is likely to naturally occur in OTHER areas of the DNA strand where the person is not of the ethnicity you are targeting. Normally, this is a very good thing and why medicine works; caffeine (for example) is chemically similar to a neural trigger that tells the brain it's tired. Caffeine bonds with those receptors, but doesn't contain the payload that triggers the tired effect, which is why coffee perks you up. It doesn't actually perk you up at all, it just stops the normal body processes from telling you that you're tired. Most medicines work the same way, tricking the body by bonding with certain receptors to trigger a specific effect and force the body to combat the infection. This is why herbal treatments, etc. also can work - they all take naturally occurring organic compounds and re-purpose them inside your body.
In practical terms, this just means that your disease isn't as likely to keep to your original plan as you might think, and it could go beyond humans as well if you're not careful. Do you really want to be the mad scientist responsible for the extinction of cows, for example?
3) Not Everything's in the Genes
In a modern world of mass global communications, behaviour has very little to do with ethnicity any more. While it's safe to say that your mad scientist is misguided, even if she genuinely believes that wiping out that ethnicity is a good thing you're forgetting that we as a species have started to heavily overlap among the races. Not only do you have the 'mixed race' problem with your viral targeting, but what about adoptions? Many of the people who identify with a specific ethnicity may not have any of those genes whatsoever. In other words, wiping out a race doesn't wipe out the thinking or behaviour that's the REAL target of your weapon.
4) Testing & Containment
If you really want this disease to target a specific segment of the community, you actually want to run clinical trials. Unfortunately, hiding the trials behind some other drug trials is going to be VERY hard in a modern society. You need both positive and negative subjects (people you want to kill and people you want to keep) in large numbers and you can't have them out in the open because this is not a treatment; it's an antigen and the last thing you want is this thing getting out into the wild before you're sure it works the way you think it should.
There are heaps of movies that explore this very scenario. There's a reason they're called horror movies. Putting that aside for the moment, you can't just kidnap the thousands of people you want to use as subjects and have them disappear for a couple of months. If your mad scientist is an Army doctor it might be more practical, but do you really want to test this on your protection should society fall apart as a result of this thing being released?
5) Mate's Rates
Even if you're doing this for ideological reasons, someone out there in your support team has a friend who's a part of this ethnic group. There will always be an attempt to protect at least one person from the release of this disease and that's also going to be a vector of weakness. Your own people will turn against you when their friends start dying as well, regardless of how much they believe in the cause. Add to that the fact that most people's genetic heritage is nothing like what they think it is and contains several closet's worth of skeletons, and you may well even kick an own goal without realising it. But that aside, individuals will cause your undoing because an individual has good character & qualities and friends. A 'race' might not. That will stir up enough conflict in most people's minds to trigger hesitation when the rubber of your plan hits the road.
Seriously, if this could be done there would be people out there doing it right now. Not sane people I grant you; this is very dangerous work we're discussing. But, ultimately there's always someone who'll survive, or you want to survive, that will throw a spanner in your works. Diseases just aren't as precise in their targeting as we'd like from a treatment and cure perspective; deliberately creating one, even one that you're trying to narrow the focus of for infections, is just plain reckless, stupid, and impossible.