Apparently not this year. Usually the Randall's on Louisiana in Midtown is open.....but alas, not this year. All other majors I've tried are closed. You might find an Asian-owned convenience store......
Most Asian/Far East Asian grocery stores are open...remember 1 store needed a cop to shut down during hurracaine? Randall used to open on X'mas day 'til 5pm. Some Walgreen..not grocery...work even harder than the post office...24 hrs..E-V-E-R-Y-D-A-Y!
If you have a Jewish part of the city there is perhaps one there that might be open part of the day, we have one such grocery store here in Dallas, TX.
Walgreens is open. I just left there 0930 hrs Christmas morning. Cleaned them out of canned hams thanks to my soon to be no more mutt. Got a prepaid cell phone for a last minute gift too. You won't be the only shopper there either.
Merry Christmas