Authorities have said the areas need to be restricted for public health reasons.
But there’s concern the government is trying to silence criticism for its handling of the environmental crisis.
Volunteers have been the backbone of the clean-up effort. They have used spades, buckets and made anti-pollution booms from sugarcane stalks and hair to absorb the oil.
Much of that work has stopped according to a video filmed by a volunteer Tushaar Daiboo at Bois des Amourettes showing abandoned drums full of the collected fuel.
Mr Tushaar and others say the government is restricting their access to affected areas.
Prime Minister Pravind Jugnauth declared an environmental state of emergency after the oil spill began. This included restrictions on movements to the areas affected for health reasons as the waste is toxic.
Those who violate these rules could face a $2,500 (£1,800) fine and up to two years in prison.
Mauritians believe that the government was slow to react as the shipwreck was left near the shoreline for two weeks before it started leaking its fuel.
Prime Minister Jugnauth told the BBC they were following expert advice.
Some environmentalists are worried that politics could overshadow the immediate crisis. Thousands of species are at risk as the oil spill happened near two protected marine ecosystems and the Blue Bay Marine Park reserve, which is a wetland of international importance.