I was going to start a similar thread. Mind if I add my question here, since it's similar?
The Jcrew cardi I am wearing in my "WiW More Hot Pink" is one of my all-time favorites. Yesterday as I was pulling it off, I felt something tear. I discovered to my great sadness that I now have not one but TWO holes at the elbows on one sleeve. The holes are bigger than your hole here. The cardigan is some kind of cotton knit too. I really want to figure out a way to salvage it. Here are my thoughts -- maybe one of these might work for you as well? Otherwise I will be following the thread for more ideas:
1) One of those iron-on mending patches, applied on inside so it doesn't show. I have done this with great success in the past. It would likely work on your sleeve as well, since your hole looks more like a slit? Since my cardigan has a busy pattern, even if the patch shows through a bit it probably wouldn't be noticed. Downside: I will know the patch is there. I'll feel it against my skin. The patches are stiff.
2) Darning it. Either do it myself, or take it to the tailor or dry cleaner. I no longer have the matching sweater thread that came with it when I bought it. But brown regular thread might work. Downside: it never quite looks the same, and if you don't use the same sweater thread, it can pucker, in my experience. Especially if darning a larger sized hole (which is case for me -- your sleeve tear is much smaller).
3) Having the sweater sleeves shortened, so they are above the elbow. This would remove the holes entirely. Downside: I kind of like the 3/4 length; it's rare for me to find 3/4 length sleeves that are just the right length. I can't tell by your photo if removing the sleeves on your top would work?