The number of positive cases has also risen to 8 and includes one death.
As of yesterday 241 people had been tested and 233 were negative.
The ministry said the three cases reported by Mashonaland East province were included in the 8 as they were reported as Harare cases because they were managed at Wilkins Hospital in the capital.
Two of those who contacted the virus from the man who travelled to Dubai are female, one aged 40 and the other 24.
While there has been a lot of publicity around media personality Zororo Makamba and the number of people he came into contact with before he died, so far only one of those he came into contact with has tested positive, according to the ministry report.
Zimbabwe introduced a 21-day lockdown to curb the spread of the coronavirus and it successfully kicked off yesterday.
President Emmerson Mnangagwa said the lockdown was not a punishment but was meant to save lives.
“This 21-day lockdown is not a punishment, it cannot be avoided. It is an opportunity to save lives,” he told the nation yesterday.
“We have 21 days right now to save thousands of lives. And how will we save those thousands of lives? By acting responsibly and by staying at home. By washing your hands and by keeping at least a 2 metre-distance from one another.
“I want all of you to spend the next 21 days acting as if you already have the virus, as if you are a carrier. Would you want to infect your friends? Would you want to infect your countrymen? Of course not! So keep your distance-two metres away from each other. Don’t touch your face. Again, wash your hands. Stay at home.”
Some Zimbabweans have complained that if they do not die of the virus, they will starve.
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