I'll break this down a bit as there will be stages to an event like this happening.
I will be placing this in the UK as no country was specified
A few hours after the supermarkets disappear
Media cover would be all over the place, when people see this they will rush to the nearest place that sells food (go for the canned food, it lasts longer) and raid it, nearly all small stores would be looted and a large amount of damaged caused to the store in the process.
The public services, Police/NHS (possibly fire brigade but unlikely, they are more likely to help with helping locals with minor issues) will be bombarded with calls, either about "why this is happening?", "Where can I get food/supplies?" etc etc.
A day after the event
The Government would
do nothing for a few days till people came banging on their doors pitch-fork-in-hand likely have local police (possibly the army if things get real bad) handing out rations and to keep peace best they can. Police would have to be more lenient with people as the lost of an immediate food souce would scare people and they wouldnt be thinking straite.
There would be a few deaths but they would be few and most wouldnt be caused directly by the supermarkets disappearing
A few more days after the event
Google defines a supermarket as:
a large self-service shop selling foods and household goods
So, after a few places try to setup their own supermarkets and they disappear people would rely on either food only shops(Butchers and the like) to get food/get food directly from a supplier/looting from other people (Doubt that this would happen but some people may do it)
The initial shock would have worn off by then and people would start going back to work (most would do this reluctantly as they need money). The disapperance of supermarkets wouldnt impact too many jobs, but if you are working in a supermarket you better fire up that CV as you are going to need it.
(I was going to list a % of the job in the UK that are directly related to supermarkets but a quick search brought nothing up, if anyone has this please link in the comments)
A week after the event (maybe a bit longer, its your time scale)
People are resigned to the fact they no longer have supermarkets for convenience.
The Government would have issued a statment (several of them proberly) stating what is going on and how people can get food/clothing and all manner of items supplied by suppermarkets.
Suppliers would have a huge increase price (their demand would be abount the same but it would be thousands of individual orders rather than 1 big one, their logistics will have a headache for a while)
After it all life would continue as normal, we have lived for a few thousand years without them, if they just change form it wouldnt cause any long lasting damage (suppermarket to Supplier)