They have been operating one clinic in the capital of Harare and another in the town of Mtoko in the northeast part of the country, Radio France Internationale reported.
The Allen Temple Baptist Church in Oakland, Calif., has been working with Zimbabwean Aids orphans for a decade, church minister Theophous Reagans said.
"We're African-American," Reagans told RFI. "We feel a strong connection with the African continent in general, and have enjoyed a wonderful relationship with the people of Zimbabwe and the authorities."
Reagans said the group also does humanitarian work in South Africa, Sierra Leone and Haiti.
This is the first time questions over licensing have been raised, he said.
Swim Week Miami Beach 2014 [PHOTOS]