.I assume that you will need to be able to use that passage and the walls as you said are soundproof enough.
Then you need something like a door or a hanging curtain.
To stop the sound you would need some mass and you can also add some absorption into your room.
I suggest you start with the following:
1 - place the refrigerator on a rubber mat - that will decouple it from the floor and cut sound transmission this way;
2 - hang a heavy curtain. you can use mass loaded vinyl http://www.vocalboothtogo.com/acoustic-and-soundproofing-products-vocal-booths/soundproofing-materials/limp-mass-barrier-mass-loaded-vinyl-for-vocal-booth/6-17
or a Mass Loaded Vinyl with Acoustic foam (fire retardant) : http://www.vocalboothtogo.com/acoustic-and-soundproofing-products-vocal-booths/soundproofing-materials/advanced-soundproofing-and-sound-absorption-panels/6-18
3 - when you hang the curtains you can hang them from BOTH sides of the passage wall this will have two-side effect - it will double the sound blocking mass and it will create layered barrier with layers of different density.
4 - make sure that your curtain overlaps the opening and creates a tight (as much as you can) seal around the edges. if you can see a light through your cover - the sound will leak through it.
5 - and lastly I am not sure looking at your drawings if the refrigerator sits just in one corner of the room, but is you can you can enclose the refrigerator itself (just on the side facing your room with sound absorbing or sound blocking materials. Do not enclose the whole refrigerator – in needs air exchange to function But if you put another barrier in the direction of your room – it will help.