I guess it'd depend on the specific capabilities of the MSDM, but I imagine something like a larger version of the Starstreak might be feasible:
https://youtu.be/D9qJg3wecH0?t=85Basically it works by getting close to the target, then releasing 3 tungsten darts which each have semi-active laser guidance systems. With modern electronics you could probably give them IR seekers.
Or, if you packaged it more like a cruise missile, you could have the main stage of the missile moving subsonic when it gets near the outer engagement envelop of the MSDM, then deploy little boosted-to-Mach 3 darts while the subsonic missile platform provides laser illumination.