CARACAS, Venezuela—President Nicolás Maduro’s government has begun dismantling price controls, a major policy shift that aims to ease widespread unrest by letting shops sell food at market prices but is worsening Venezuela’s already punishing inflation.

What began as a limited experiment in March in western Zulia state, which borders Colombia, has since been rolled out to six other border states, according to ruling-party governors and interviews with supermarket owners and shoppers across the country. One of the governors...