Manufacturers have compounded the crisis after they stopped producing goods.
They say the official price freeze is not viable given the price of other goods and raw materials continue to skyrocket.
Police had to be called in at a supermarket in central Harare early on Thursday to control a huge crowd that had jammed the shop after word quickly got round that sugar was available.
"Wholesalers and retailers should desist from allowing bulk buying of basic commodities," Obert Mpofu, the trade and industry minister, told the Herald newspaper after Wednesday's buying frenzy.
Spiralling prices have pushed inflation above 4,500 per cent, the highest in the world and the value of the local currency has plunged thanks to a thriving black market.
The country is in the throes of an eight-year economic recession that has hit workers in urban areas the hardest and caused shortages in foreign currency, fuel and food.
Mugabe denies charges he has presided over the country's worst economic crisis since independence from Britain in 1980 and instead says the West has sabotaged the economy to punish him for seizing white-owned commercial farms for black citizens.
Some people have now formed teams to trawl shops in Harare and buy whatever basic goods they can in bulk.
More than 200 business people, including a ruling party senator, have been arrested for defying the price freeze, which economic analysts say will only strengthen the black market.
Police also said they had unearthed huge quantities of sugar, soap and cooking oil - all in short supply - at a site in Harare and suspect the goods were being hoarded to create artificial shortages in the market.
"The public is urged not to be involved in panic buying of commodities whose prices have been reduced, as sustainable continuous supplies will be provided," Sikhanyiso Ndlovu, the information minister, told the Herald.