Isolation between measuring voltage from low current circuit?
Based on your answer, you're looking at a chip solution like this: ISO124. It's crazy expensive, but you can find other cheaper options with lower isolation ratings.

Either way, you definitely need a way to power the amplifier from "the other side", as in the side where the device under test is. If it's totally unworkable to have a power source on the DUT side, I don't think it's logically possible. 

WARNING: I am not trained in creating life-critical/cannot fail type equipment (I don't even know the official name for this!) and my advice comes with NO WARRANTY.