"Because of the speed with which the patient was identified and isolated, and the identification of all the other bus passengers coming from Butembo, the risk of it spreading in the rest of the city of Goma is small", the ministry said in a statement.
The person with the confirmed case is a pastor who had been in the town of Butembo, said the press release by the health ministry.
The head of the World Health Organization, Tedros Adhanom Ghebreyesus, said the development was so worrying that he was reconvening the agency's emergency committee as soon as possible "to assess the threat of this development".
The health ministries in Congo's neighbors have been preparing for months for the possibility of cases, and frontline health workers already have been vaccinated.
Congolese police guard a health center while Ebola vaccinations take place.
Since November, more than 3,000 health workers in Goma have been vaccinated for Ebola and trained in the detection and management of Ebola patients.
Now health authorities along his route are trying to hunt down all those he may have been in contact with after the man became Goma's first confirmed Ebola case on Sunday.
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The ministry announced Sunday that a sick pastor had arrived in the regional center by bus from the northeastern city of Butembo, where the virus first struck last September.
A worker from the World Health Organization decontaminates the doorway of a house in the village of Mabalako, in eastern Congo last month.
Other times the violence against health teams has come from residents who do not want their loved ones taken to treatment centers or buried in accordance with guidelines aimed at reducing Ebola transmission.
In Geneva, WHO chief Tedros Adhanom Ghebreyesus said he planned to reconvene the agency's emergency advisory board to assess whether the outbreak should be declared a "public health emergency of global concern" - a move that ramps up worldwide response.
Health workers dressed in Ebola protective suits are seen as they prepare an ebola preparedness facility at the Bwera general hospital near the border with the Democratic Republic of Congo in Bwera, Uganda, June 12, 2019. Yet, despite these exhaustive preventative and treatment efforts, fighting Ebola has proved hard because of community mistrust, limited health care resources, difficult-to-access locations, and violent attacks on heath care workers.
Ebola causes diarrhoea, vomiting and hemorrhagic fever and can be spread through bodily fluids. The current outbreak is the second worst ever, after an epidemic between 2013 and 2016 killed more than 11,300 people in West Africa.
That raised fears Ebola could accelerate into one of Africa's most densely populated areas and over the Rwanda border.
Mark Lowcock, the United Nations humanitarian chief, said without increased resources it would not be possible to bring the epidemic "under control".