There is no standard minimum dimension between counters and islands in kitchen design.

I usually make the clearance 3-6. 3-3 can work if the stove or dishwasher is not directly across from the island.

IMHO the critical issue is that when someone bends over to open an oven they should not bump their rear end against the island hard enough to cause them to lose their balance. Everyone has to decide what that is on their own and large designers tend to have different opinions from small ones.

People usually stand to the side of a dishwasher so clearance between the open door and the island is critical. Avoiding putting the dishwasher directly across from the island is often a good idea.

You didn't indicate what happens on the other side of the island.

jaya, you need to discover the kitchen forum. Come on over. :-) In fact, search the archives, I know people have asked the same question before.

FWIW, I've got a 13' wide kitchen and the 2' island is fine.

These are the two tightest kitchens islands I've ever designed. The owners have been very happy with them.

OP may come up against the normal groupthink that exists in any community, and which absolutely does exist in the kitchen forum : I'll bet my boots that almost ALL the regulars will chime in that it's a tight aisle at only 3 feet, and giving that kind of input won't help or encourage. The best advice has already been given, above. Three feet is enough for one person, or two who are willing to coordinate. (Yes, if several people want to work there at the same time, they'll need to work it out somehow, coaching or communicating to achieve harmony and choreography.) On site, in person, nobody complains. On paper everyone will question it when they see the numbers. Saying it that way is paraphrasing Sarah Richardson :
"Minimize allowances
... I tend to push the limits by reducing the clearance (usually not less than 36 inches) in favor of achieving more counter and storage space. Lets face it, preparing meals is not a group effort in most homes, and there doesn't need to be enough space to choreograph a dance routine. In all my years of pushing the limits, no one has ever complained after their kitchen went in (it only seemed to be a problem on paper). ...."
It's the second to last paragraph in her article linked to below.

Here is a link that might be useful: Sarah Richardson on HGTV

Apparently the OP took the issue to the kitchen forum and then lost interest.