In 2014, we stayed a few nights at Laugavegur 18 in Reykjavik. A few blocks down that same street, we shopped at a fairly large grocery store which I think was decorated in a bright yellow storefront - I'm sorry that I don't recall the name of the store nor the hours. I was able to purchase some gluten-free items for my celiac husband which was the main objective for finding a grocery store. I was impressed that their frozen foods section was an entire room!
Maybe another poster will be able to provide more details?
Edit: Just looked at the previous poster's entry, and the store I went to may have been named BONUS. Their website is not in English, but as far as I can tell, it looks like they are open on Sundays.