Officials say the dead include a police officer who was stoned to death by protesters in Bulawayo city, while two people died during protests over fuel price hike in Chitungwiza and Kadoma towns.
Three people, including a police officer, were killed in Zimbabwe on Tuesday during protests against a sharp hike in fuel prices, police spokeswoman Charity Charamba said.
The police officer was stoned to death by protesters in the city of Bulawayo, while two people died during protests in Chitungwiza, a town south of Harare, and Kadoma, a town 141 km west of the capital, Charamba said.
Separately, Zimbabwe's Information Minister Monica Mutsvangwa said she was not aware of an alleged shutdown of the internet.
Zimbabwe is embroiled in protests and riots as civilians contest more than doubled fuel prices and poor economic conditions.
Living allowances announced
Earlier, Labour Minister Sekai Nzenza promised public workers a cost of living allowance of between five percent and 23 percent of their monthly salary, she told Reuters news agency on Monday, against a backdrop of strikes and violent protests in the country over fuel price hike.
Sekai Nzenza said by phone that the allowance will be issued from January to March while negotiations with unions continue.
While a 40-day doctors strike ended last week, teachers remain on strike and civil servants have also threatened industrial action.
Protests over fuel price hike
Meanwhile, a Zimbabwean military helicopter on Tuesday fired tear gas at demonstrators blocking a road and burning tires in the capital on a second day of deadly protests.
Soldiers moved in to disperse crowds at the busy intersection and transport hub in Harare amid Zimbabwe's biggest unrest since deadly post-election violence in August.
TRT World's John Nyashanu has more from Harare.
Witnesses also reported violence in the eastern city of Mutare, where people attacked passenger buses and destroyed some shops.
Social media such as Facebook, Twitter and WhatsApp were disabled.
Businesses and schools were shut down and public transport vehicles were grounded in most of the country despite government assurances that security would be provided.
The government over the weekend announced a price of $3.11 per litre (0.26 gallons) for diesel, and $3.33 per litre for gasoline.
That means gasoline in Zimbabwe is now the most expensive in the world, based on data from GlobalPetrolPrices.com .
The site says Hong Kong had the highest price for a litre of gasoline on January 7: $2.04.
Deaths in unrest
Five people were killed in Monday's unrest during which security forces opened fire on crowds, according to the Zimbabwe Association of Doctors for Human Rights.
Another human rights group said 26 people suffered gunshot wounds and that some were afraid to go to hospitals for fear of arrest or assault.
Lives were lost, police officers were injured, property was damaged and more than 200 people were arrested, said Owen Ncube, the state security minister.
He blamed the main opposition MDC party and some civil society groups for stoking violence in an attempt to topple the government of President Emmerson Mnangagwa, who took power after longtime leader Robert Mugabe was forced to resign in November 2017.
The Zimbabwe Congress of Trade Unions had called for a three-day national shutdown to protest against the fuel price increase announced by Mnangagwa, who then left for Russia on a multi-nation trip to try to attract international investment.
He is set to attend the World Economic Forum in Davos, Switzerland.
Opposition headquarters attacked?
Police and soldiers barged into homes in some Harare suburbs and assaulted people, according to Zimbabwe Lawyers for Human Rights. The MDC party said its headquarters was attacked.
The opposition and other groups supporting the shutdown urged people to stay indoors rather than engage in street action.