Not necessarily. Prices have lots of downward pressure right now (Producers are eating increasing costs of commodities in some cases) in order to stay competitive with one another and/or to maintain volume/revenue. Plus, many stores with jobs that would be affected would already likely be paying more than minimum wage to their employees anyways (Example in CA: Checkers at Safeway make more than minimum wage - bag attendants might not, not sure). Same with food preppers at a fast food joint. The places primarily involved in hiring minimum wage employees are typically dependent on low price points to begin with to maintain and increase foot traffic. It's not in their interest to increase prices more than other competitors so if one company eats the cost of paying their employees more and does nothing on the price point side of things their profitability might decline if traffic stays the same but if a competitive advantage can be had then there's potential to make more money by appealing to more consumers.
That's just one facet of how minimum wage can work too. Thedude has far more knowledge on the topic than I.