The recommendation comes after more than a dozen European countries suspended use of the AstraZeneca vaccine amid concerns over the risk of blood clots.
John Nkengasong, director of the Africa Centers for Disease Control and Prevention, told a news conference the "benefits still outweigh the risks" and countries should "move forward".
Africa CDC Director John Nkengasong said the 16 countries had asked for a total of a total 114 million doses under the AU's Vaccine Acquisition Task Team (AVATT).
"Our hope is that in the next two to three weeks, they should be having their vaccines," he told a virtual news conference.
Africa has not started vaccinations and there is concern that more prosperous regions will get an unfair head start in the global fight against COVID-19.
We should not see vaccines as a magic bullet for now, it will take time for vaccines to be rolled out in a way that we have herd immunity.