You will probably have to build a new array.
Fortunately you can avoid python loops for this task, using fancy indexing:
h, w = 20, 10
A = np.arange(h*w).reshape(h, w)
del_ind = np.random.randint(0, w, size=h)
mask = np.ones((h,w), dtype=bool)
mask[range(h), del_ind] = False
A_ = A[mask].reshape(h, w-1)
Demo with a smaller dataset:
>>> h, w = 5, 4
>>> %paste
A = np.arange(h*w).reshape(h, w)
del_ind = np.random.randint(0, w, size=h)
mask = np.ones((h,w), dtype=bool)
mask[range(h), del_ind] = False
A_ = A[mask].reshape(h, w-1)
## -- End pasted text --
>>> A
array([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11],
[12, 13, 14, 15],
[16, 17, 18, 19]])
>>> del_ind
array([2, 2, 1, 1, 0])
>>> A_
array([[ 0, 1, 3],
[ 4, 5, 7],
[ 8, 10, 11],
[12, 14, 15],
[17, 18, 19]])