Raising the minimum wage does not affect overall price inflation. It merely shifts entrepreneurial demands away from low-wage labor and toward capital equipment and higher-wage labor. To the extent that the reduced production of output increases price of goods produced by minimum-wage labor, consumers must demand less of other things to maintain their demands for such output. Prices go up on some goods and down on other goods.
Monetary inflation which causes price inflation will, as you suggest, reduce the impact of a particular level of the minimum wage over time. As the general purchasing power of the dollar falls, a given level of minimum wage declines relative to the rising prices of other inputs. As a result, the unemployment generated by a particular level of the minimum wage is reduced over time.
Here’s a wiki on minimum wages: