The Restaurant owner is making a simple mistake. He has taken Pre-MinWage circumstances and applying them to Post-MinWageHike circumstances.
What people were willing to Pay for your food wasn't based on the Amount it Cost alone, there is no fixed price for Item X. It was based upon His Price in comparison to his Competitors Price. All his competitors will also have to raise their prices accordingly, once again restoring the Norm.
As has been mentioned, there will also be new customers able to buy the food he is selling. Greater the pool of potential customers, the greater Demand there will be for his food.
That said, there can be somewhat of a consumer sticker shock at first. That is, that previous customers will see the new Prices and think twice about purchasing as much as they used to. However, in time they will accept it.
A similar sort of phenomena happened here in Canada when we introduced our National Sales tax(GST- Goods and Services Tax). For 6 months to a year there was a decline in Consumer activity, but after that time people adjusted and consumption returned to normal levels. The same sort of phenomena will occur when any Price goes up. Similarly, over the last 15ish years we have seen how consumption rises/falls based upon the wild fluctuations of the price of Oil. People always adjust though, Demand for prepared food and other consumables always recovers.