It depends....

• Is this a one-person or multi-person kitchen?

  If one-person all the time, no exceptions AND it's not a major traffic path through the kitchen AND there's no seating on the aisle, then yes, 36" is probably fine.

  If more than one person will be working in the kitchen, then see the next questions...

What's on the counter? What's on the island?

If they both have a major appliance (range/cooktop/oven/DW) and/or fixture (prep sink/cleanup sink) or a primary work Zone (Prep Zone, Cooking Zone, Cleanup Zone), probably not. Try for at least 42", 48" would be better.

If only one Zone or major appliance or fixture AND it's not a major traffic path through the kitchen AND there's no seating on the aisle, then it's probably livable...but I would still try for 42".
Is it a major traffic path through the kitchen?

If so, no, it's not. Try for at least 48", preferably 54".
Is there seating at the island on that side?

If so, no, it's not. Try for at least 50", preferably 60"...with a 15" seating overhang.
Is this for resale?

If so, no. I would try for 42".

I suggest you post your layout here for review & comments...but only if you're willing to change things or at least discuss changing things if problems are found.

Part of that answer depends on the space, layout, traffic flow, number of people and size of people working in the kitchen and the relative space in the rest of the kitchen. There are folks here who want 4 feet or more and even 42" can give you a bit more ease in working spaces, but I had 36" between my sink and cooktop wall before we remodeled and I have a whopping 37" now. My biggest complaint was not that the space was too narrow but that the builder put the sink and cooktop right across from each other and DH had a thing for getting at the sink and wanting to prep or do dishes when I was at the cooktop. By moving the cooktop to the wider side of the kitchen, I got less conflict at the sink and a wider space in front of the cooktop -- 40" counter to counter, but only 36" if you count the big ol' knobs on that thing. I'm 5'12" and can move about quite easily in this kitchen. To me, it is efficient and I am just glad I could improve on the use of the existing space -- there was no where to go in any direction. It's not a huge kitchen and the spaces seem to be in scale with one another.

If you have the option of reducing your island a bit and giving yourself more clearance, you might like having a little more room. My island is only 34" in cabinets and 37" overall. That is a 21" deep vanity depth base on one side and a 13" (upper depth on a toe kick) cabinet back to back. The space is very functional, but that extra inch on the shallower side make a big difference -- I can store my blender, waffle iron, crockpot, ice cream maker and even a Kitchenaid stand mixer as well as dishes and glassware in those cabinets. My trays wouldn't fit there, but most anything else in my kitchen would and it's very user friendly space.