Prices are not set by the cost of production but by supply and demand. In a healthy market the cost increase of a wage minimum cannot affect the prices, it may only make it uneconomical to produce certain goods (but this almost never happens because margins aren't usually that tight). What the minimum wage actually amounts to is wealth redistribution, from the holder of capital to the provider of labor. It doesn't change the amount of goods and services sold, it just affects who is buying them.

Like all social redistribution schemes, it can be good if wealth isn't distributed equally enough for healthy market interaction, and harmful if wealth is distributed too equally for market incentives to exist.