Yes, but only indirectly.
Inflation is a SYSTEMIC rise in prices, not a rise in fast food prices. At the system level, prices rise only when money is plentiful (i.e. "cheap") relative to the quantity of goods&services available. So, if there is 10 percent more money and 10 percent more goods&services, prices stay the same. But if there is more money (as a result of printing), prices will rise. And if there are fewer goods&services available, then prices rise.
If Pete has $5 to spend on both food ($4) and a toothbrush ($1), but McDonald's raises its prices in response to the Minimum Wage increase, Pete MAY elect to spend all $5 on food and buy no toothbrush (causing the toothbrush manufacturer to drop its prices to increase their allure) or he may still buy a toothbrush and buy less food than he'd intended at McDonald's causing its profit to fall since it now has higher employment costs, or he may skip McDonald's entirely and just eat a TV dinner, again hurting McDonald's bottom line and pressuring it to forego some of its desired profits by lowering prices back to where they were. McDonald's might close some of its stores.
The bottom line is that if there's only 5 dollars in the system and McDonald's raises its prices, the economy will be harmed but systemic prices won't change. McDonald's will either find that its attempt to raises prices was a flop, or competitors will experience a drop in demand for their products, forcing their prices down. Supply and Demand, right? Systemic prices will only increase indirectly, as a result of the weaker economy a Minimum Wage hike precipitated, not because one vendor decided to increase its prices.
I probably didn't say that as clearly as I could, but I hope you understand. Money increases relative to available goods is what causes prices to rise. If I decide to sell my pickup truck for a million dollars, it won't cause inflation. Nobody will buy it. Or, if some moron does, that's a million dollars that won't be spent on other more sensibly priced things and their prices will consequently fall, countering what happened to the price of pickup trucks.
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