The mobs also burned tires and ransacked shops in the capital. Police responded by firing shots into the crowds and the air.
S-TV, a private station, said the dead included one child.
The station said three adults were declared dead in hospitals and the other two died in the streets. The station gave no other details. It was not immediately clear if any of the six had fallen to police bullets or died from other causes.
A witness saw an ambulance remove the apparently lifeless body of a boy who had a severe head wound. The government hasn't given any casualty figures from Wednesday's rioting.
Police appealed for calm on state radio and TV and said they had made an unspecified number of arrests.
Police had declared the marches illegal, saying no group sought permission to hold them. Word had spread for days in this former Portuguese colony in southeast Africa that there would be demonstrations.
Thousands of protesters, most of them young men, lined the streets of Bagamoyo, a crowded, impoverished neighborhood just north of downtown Maputo. As they moved into the city center, they looted shops and warehouses. Protests were also reported in other areas around Maputo.
Police appealed for calm on state radio and TV and said they had made some arrests. Youths were blocking streets and ransacking property. Many public transport drivers have abandoned their vehicles in the streets.
Mozambicans have seen the price of a loaf of bread rise by 25 percent, from four to five meticais (from about 11 cents to about 13 US cents) in the past year. Fuel and water costs also have risen.
The Rome-based UN Food and Agriculture Organization said Wednesday international food prices have risen to their highest level in two years. Its food price index shot up 5 percent between July and August. That was still 38 percent down from its peak in June 2008.
Around the world, high prices have been blamed on dry weather's effect on harvests and high fuel costs incurred when moving food from producers to consumers. Some critics also say bad government decisions are making shortages worse and accuse producers of colluding to push up prices.
The FRELIMO party, in power since Mozambique won independence from Portugal in 1975, has been plagued by charges its government is corrupt and inefficient.
Violent protests over high costs erupted here in 2008, when global food prices jumped. Factors cited included a drop in the US wheat harvest and higher demand for crops to use in biofuels. After a week of clashes between police and rioters that killed at least four people and seriously injured more than 100, the government cut fuel prices.
Egypt has in recent months seen protests over rising food prices.
The UN agency said the food price surge reflected a sudden sharp rise in wheat prices following drought in Russia and the country's subsequent restrictions on wheat sales. Higher sugar and oilseed prices also were factors.
