Sorting Algorithms Optimisation Python
Instead of searching for the value that belongs at Queue[i] to swap it there, just swap the value that is there to where that belongs:
def MinimumSwaps(Queue):
    MinSwaps = 0
    for i in range(len(Queue) - 1):
        while Queue[i] != i + 1:
            j = Queue[i] - 1
            Queue[i], Queue[j] = Queue[j], Queue[i]
            MinSwaps += 1
    return MinSwaps

This improves the performance to \$O(1)\$ for using a value instead of the \$O(n)\$ for searching. And thus total performance to \$O(n)\$ instead of your original \$O(n^2)\$. Still using only O(1) extra space.