MEXICO CITY—Mexico’s minimum wage will rise almost 10% on Sunday, in a jolt to the system meant to stoke the poorest workers’ buying power, which has been eroded by recessions and past bouts of high inflation.

But the prospect of higher earnings is doing little to dent pessimism among consumers, who head into 2017 facing rising fuel costs, higher interest rates and a weakening peso that closed 2016 near record lows against the U.S. dollar.

Labor,...