The first 300 doses were administered on Tuesday near the border with the Democratic Republic of Congo, a spokesperson for the AU's Centres for Disease Control and Prevention (Africa CDC) told AFP.
The DRC has been the worst-affected country, with nearly 22,000 cases and more than 700 deaths linked to the virus between January and August.
On a call with reporters, Africa CDC director general Jean Kaseya said vaccinations would start in the DRC in "the first week of October".
Mpox, previously known as monkeypox, is caused by a virus transmitted to humans by infected animals that can also be passed from human to human through close physical contact.
Deadly in some cases, it causes fever, muscular aches and large boil-like lesions on the skin.
The World Health Organization (WHO) last week prequalified an mpox vaccine, MVA-BN, for the first time, paving the way for the United Nations and other international agencies to procure them.
The Africa CDC says there has been a total of 29,152 cases and 738 deaths across 15 countries on the continent.
"Mpox is not under control," said Kaseya.
A CDC spokesperson added that testing remained an issue, with only half of suspected cases tested, and said the agency was aiming for more than 80 percent.
WHO's chief Tedros Adhanom Ghebreyesus warned in a briefing Thursday that they were not dealing with one outbreak, but "several" in different places, caused by different strains.
In particular, he highlighted the situation in Burundi and the DRC "where cases are continuing to increase".
According to the WHO prequalification, the vaccine can be administered to people over the age of 18 as a two-dose injection given four weeks apart.
With most mpox cases and deaths in the DRC in children, the WHO stressed the vaccine could be used "off-label" in infants, children and adolescents, as well as in pregnant and immunocompromised people.
"This means vaccine use is recommended in outbreak settings where the benefits of vaccination outweigh the potential risks," the WHO said in a recent briefing.
The agency also recommends single-dose use in outbreak settings where supplies of the vaccine are constrained. But more data is needed on vaccine safety and effectiveness in such circumstances, it stressed.
The currently available data showed that a single dose of the MVA-BN vaccine given before exposure had an estimated 76-percent effectiveness in protecting against mpox, it said. Two doses were estimated to be 82 percent effective.