Product dimensions: 12" W x 9"D x 15"H
However, with the frother open (it unfolds from the left side of the machine) the width increases to 15.5", plus you probably need another inch for your cup to fit, so say 16.5".
Also, you will need an additional 2" on the top in order to be able to remove the water reservoir.
Therefore, your opening should be at least 16.5"W x 9"D x 17"H.