The shortage is causing frustration among traders and consumers.
The BBC reported that most shops in the country have run out of sugar and the few that are still selling are charging almost double the normal price.
The Tanzanian government has attributed the shortage of the commodity to the coronavirus pandemic. The government says the pandemic has disrupted importation schedules.
However, the government also blames some business people who have hoarded sugar to create a false scarcity so that they can sell it at an increased price.
Tanzania imposed price controls for sugar in April after a decline in local production due to poor weather conditions.
A kilogramme of sugar for domestic consumption was set at 2,700 Tanzanian shillings ($1.17), but traders said it was unprofitable.
On Monday, around 1,500 tonnes of sugar arrived at the port of Dar es Salaam.
The director of the Tanzania Sugar Board, Kenneth Bengesi, said they would soon start distributing across the country.
Data from 2016 showed that Tanzania consumes 590,000 tonnes of sugar annually for both domestic and industrial consumption. But the country produces an average of 300,000 tonnes every year.
The shortage of sugar is not new in the East African country.
The poor weather conditions and price disagreements between the government and traders have often in the past caused scarcity and sharp increases in prices.