It says South Africa – where testing has been widespread – accounts for more than half of all cases.
Tanzania’s lack of data meanwhile is a “concern” for the AU.
Experts say a lack of comprehensive testing across Africa means the true extent of the pandemic is not known.
Tanzania, for example, has not published figures for weeks and in early July its health minister said the virus was “heading towards an end”.
“We continue to reach out [to Tanzania] but we’re not having the right responses,” director of the AU’s Centres for Disease and Control and Prevention (Africa CDC), Dr John Nkengasong, told the BBC.
In the continent overall, more than 22,000 people have died with Covid-19 and almost 690,000 people have recovered, the figures show.
Just over eight million tests have been carried out, but Dr Nkengasong said at least 13 million tests should have taken place.
Africa’s first coronavirus case was confirmed in Egypt in February – three weeks after Europe, and two months after the outbreak began in China in December.
Where are Africa’s hotspots?
The two countries with the highest numbers of cases are South Africa and Egypt. They accounted for 75% of all the new cases reported by mid-July.
South Africa has the highest recorded number of total cases and reported deaths, and make up more than half of all the cases in Africa.
The Africa CDC is keeping a close eye on Nigeria, Ghana, Kenya, Ethiopia, Sudan, Zambia and Zimbabwe, Dr Nkengasong told the BBC’s Newsday programme.
More than 65% of Africa’s 55 countries have reported fewer than than 5,000 cases, Africa CDC says.
What is being done?
African nations have been praised for locking down more swiftly than other parts of the world.
But there are concerns about insufficient testing, and the Africa CDC admits this should be expanded along with tracing.
Dr Nkengasong said another risk was “community fatigue” where people tire of prevention messages.
“We know that wearing masks constantly will help this situation,” he added.
A coronavirus vaccine developed by the University of Oxford and tested in South Africa, the UK and Brazil, appears to be safe and triggers an immune response.
But it is still too soon to know if this is enough to offer protection and larger trials are under way.