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4 year oldUN officials also say it is likely the pandemic will kill at least 300,000 people in Africa and push nearly 30 million into poverty.
The past week in Africa has seen a sharp rise in coronavirus cases.
There have been almost 1,000 deaths and almost 19,000 infections across Africa, so far much lower rates than in parts of Europe and the US.
The UN Economic Commission for Africa - which warned 300,000 could die - called for a $100bn (£80bn) safety net for the continent, including halting external debt payments.
The WHO says the virus appears to be spreading away from African capitals.
It has also highlighted that the continent lacks ventilators to deal with a pandemic.
More than a third of Africa's population lacks access to adequate water supplies and nearly 60% of urban dwellers live in overcrowded slums - conditions where the virus could thrive.
There are almost 19,000 confirmed cases in Africa and at least 970 confirmed deaths across the whole continent, which has a population of about 1.3 billion.
North Africa is the worst affected region. Algeria, Egypt and Morocco have all had more than 2,000 cases and at least 100 deaths. Algeria has had the most deaths, with 348.
Elsewhere, South Africa has also had more than 2,000 cases, with 48 deaths, while the continent's most populous nation, Nigeria, has had 442 cases and 13 confirmed deaths out of a population of some 200 million.
Get the latest on the BBC's live tracker.
WHO Africa director Dr Matshidiso Moeti told BBC Global Health correspondent Tulip Mazumdar that international travel played a part.
"If you look at the proportion of people who travel, Africa has fewer people who are travelling internationally," she said.
But now that the virus is in within Africa, she says that her organisation is acting under the assumption that it will spread just as quickly as elsewhere.
The WHO has witnessed the virus spreading from big cities to "the hinterland" in South Africa, Nigeria, Ivory Coast, Cameroon and Ghana, Dr Moeti said.
There are around 15 African countries where the virus has not spread far so, if these countries adopt strong social distancing measures, they could contain the virus, she added.
By Anne Mawathe, BBC Africa Health editor
Since the first case was reported in Africa, most of those infected have been concentrated in urban areas where health facilities and access to care is in close proximity.
This cannot be said of rural areas where treatment facilities are scarce or non-existent.
The fragile health infrastructure in the continent means that it will be doubly strained by an increasing number of new Covid-19 infections.
If the experiences of countries like Italy, Spain, France and the US are anything to go by, then Africa will struggle to manage an increasing number of people suffering from the virus especially those who need critical care.
Healthcare workers in different parts of the continent have complained about the lack of adequate personal protective equipment.
Covid-19 is a highly infectious disease and healthcare workers are at a higher risk of infection.
Tunisia already has 68 healthcare works infected, Liberia has 18 while Niger is reporting 32.
Provisional projections from the WHO suggest that more than 10 million people could be infected in the next 3-6 months, but that figure doesn't take into account public health measures that are being put in place.
If Covid-19 is able to take hold on the continent, the consequences could be far more devastating than we've seen in Europe and the US, says our global health correspondent.
The WHO says there are only around five intensive care beds available for every one million people in most African countries, compared with around 4,000 beds for every million people in Europe.
Dr Moeti said the WHO was focusing on prevention rather than treating the virus, because many African countries don't have the capacity to treat many coronavirus patients.
"We want to minimise the proportion of people who get to the point of needing critical care in an ICU, because we know that these types of facilities are not adequate by any means in the majority of African countries," she said.
Dr Moeti said the lack of ventilators was "one of the biggest challenges" that African countries are facing.
For patients critically ill with Covid-19, access to a ventilator could be a matter of life or death.
The machines get oxygen into the lungs and remove carbon dioxide from the body when people are too sick to breathe on their own.
One of the first recorded deaths from coronavirus in Africa was Zimbabwean journalist Zororo Makamba in March.
The local authorities in the capital, Harare, said that they did not have a ventilator to treat him.
Dr Moeti pinpointed a few key things countries need to do:
Several countries have enforced lockdowns.
In some countries, schools are been turned into healthcare facilities where people can be quarantined and even offered care.
Textile industries have been recalibrated to start manufacturing personal protective equipment such as medical gowns.
Earlier this week the UN Food Programme started distributing badly needed equipment around the continent from a new hub in Ethiopia's Bole airport.
The cargo included one million face masks, personal protective equipment, and ventilators.
And the Africa Centre for Disease Control and Prevention has announced that it will roll out one million coronavirus testing kits to meet the continent's "big gap".
The organisation's director John Nkengasong says testing rates on the continent are too low.
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