Well, here is a solution if you want the background to be other than a solid black color. We only need to invert the mask and apply it in a background image of the same size and then combine both background and foreground. A pro of this solution is that the background could be anything (even other image).

This example is modified from Hough Circle Transform. First image is the OpenCV logo, second the original mask, third the background + foreground combined.

# http://opencv-python-tutroals.readthedocs.io/en/latest/py_tutorials/py_imgproc/py_houghcircles/py_houghcircles.html
import cv2
import numpy as np

# load the image
img = cv2.imread('E:\\FOTOS\\opencv\\opencv_logo.png')
img = cv2.cvtColor(img, cv2.COLOR_BGR2RGB)

# detect circles
gray = cv2.medianBlur(cv2.cvtColor(img, cv2.COLOR_RGB2GRAY), 5)
circles = cv2.HoughCircles(gray, cv2.HOUGH_GRADIENT, 1, 20, param1=50, param2=50, minRadius=0, maxRadius=0)
circles = np.uint16(np.around(circles))

# draw mask
mask = np.full((img.shape[0], img.shape[1]), 0, dtype=np.uint8)  # mask is only 
for i in circles[0, :]:
    cv2.circle(mask, (i[0], i[1]), i[2], (255, 255, 255), -1)

# get first masked value (foreground)
fg = cv2.bitwise_or(img, img, mask=mask)

# get second masked value (background) mask must be inverted
mask = cv2.bitwise_not(mask)
background = np.full(img.shape, 255, dtype=np.uint8)
bk = cv2.bitwise_or(background, background, mask=mask)

# combine foreground+background
final = cv2.bitwise_or(fg, bk)

Note: It is better to use the opencv methods because they are optimized.

You don't apply a binary mask to an image. You (optionally) use a binary mask in a processing function call to tell the function which pixels of the image you want to process. If I'm completely misinterpreting your question, you should add more detail to clarify.