Your code is \$O(n^2)\$ because of the inner loop.

for j in range(i+1,len(Queue)):
    if Queue[j] == i+1:
       # inner

We can change this to be \$O(1)\$ by making a lookup table of where \$i\$'s location is. We can build a dictionary to store these lookups.

indexes = {value: index for index, value in enumerate(Queue)

We can then just swap these indexes with your existing inner code to get \$O(n)\$ performance.

def MinimumSwaps(Queue):
    indexes = {value: index for index, value in enumerate(Queue)}
    MinSwaps = 0
    for i in range(len(Queue) - 1):
        i_value = Queue[i]
        if i_value != i+1:
            j = indexes[i+1]
            j_value = Queue[j]
            Queue[i], Queue[j] = Queue[j], Queue[i]
            indexes[i_value], indexes[j_value] = indexes[j_value], indexes[i_value]
            MinSwaps += 1
        else:
            continue
    return MinSwaps

Your code is \$O(n^2)\$ because of the inner loop.

for j in range(i+1,len(Queue)):
    if Queue[j] == i+1:
       # inner

We can change this to be \$O(1)\$ by making a lookup table of where \$i\$'s location is. We can build a dictionary to store these lookups.

indexes = {value: index for index, value in enumerate(Queue)

We can then just swap these indexes with your existing inner code to get \$O(n)\$ performance.

def MinimumSwaps(Queue):
    indexes = {value: index for index, value in enumerate(Queue)}
    MinSwaps = 0
    for i in range(len(Queue) - 1):
        i_value = Queue[i]
        if i_value != i+1:
            j = indexes[i+1]
            j_value = Queue[j]
            Queue[i], Queue[j] = Queue[j], Queue[i]
            indexes[i_value], indexes[j_value] = indexes[j_value], indexes[i_value]
            MinSwaps += 1
        else:
            continue
    return MinSwaps

There is potentially performance on the table by using a dictionary as a lookup table rather than a list. Whilst both have the same algorithmic complexity. To address this we can just build indexes as a list.

indexes = [None] * len(Queue)
for index, value in enumerate(Queue):
    indexes[value] = index