(A) I will not leave the place until the minister does not meet me. (B) I will not leave the place until the minister doesn’t meet me. (C) I will not leave the place until the minister meet me. (D) I will not leave the place until the minister meets me
A and B are incorrect. Not is already embedded in until.
Also, C is incorrect as the minister is a single person, and with a singular subject, singular verb follows(ending in ‘s’).
Thus, D is the right answer.