Perhaps you should narrow your question because Africa is a huge continent. Egyptians have used wheels for thousands of years, there are carved illustrations of pharaohs riding wheeled chariots.

Wheels were used by people who traded with the Egyptians in accordance with their suitability. Wheels are not much use over desert terrain, so camels and pack animals were more useful in transporting goods. But in places south where the terrain was suitable, for example Ethiopia and parts of the Sudan, wheeled carts certainly existed thousands of years ago.

It's true that wheels for transportation were not used in some parts of sub-Saharan Africa. I don't think we can attribute this to a lack of knowledge of wheels, and in any case, why would such knowledge arrive via Europeans, when wheels were being used in their own continent further north and east? Has anyone actually made the assertion that sub-Saharan Africa had no contact with Egypt or Abyssinia? That seems pretty ridiculous.

The explanations I've heard have to do with the non-availability of draft animals for pulling carts. This was because of several reasons. Population densities were very low, and generally pastoralists and farmers belonged to different tribes. So the adoption of animals for draft work like pulling plows or carts didn't happen. Their particular mode of farming didn't require much plowing either, because it was a bush-fallow rotation where you clear bush and plant in the clearing. The roots are never cleared, and are in any case near impossible to clear even with plows. So you just plant for a few years then the roots grow back and bush reclaims the land and you move on, only to return a few years later.

Another reason was the widespread presence of the tsetse fly and trypanosomiasis, which takes a terrible toll on domesticated animals. The disease burden is always present, and while you can herd animals if you feed them well and move them seasonally to avoid the worst of the flies, if you put these animals to work pulling carts or plows the added work stress will kill them.

It's possible that draft work was introduced several times in the past, but it didn't stick due to these problems.

The big change brought about by Europeans was the systematic clearing of land, which removed the wild animals that were the reservoirs for the tsetse fly. Prior to the Europeans, population densities were too low and tribes too divided for any large scale land clearing. As large tracts of land were cleared, pockets were created that were relatively free of the tsetse fly, where large domesticated animals could then be used for draft work.

Also, perhaps we should separate the use of the wheel into transport and pottery categories. While wheeled vehicles were not used in sub-Saharan Africa before colonial times, they certainly used pottery wheels.

While I agree with most of his post /u/EvanRWT alludes to but doesn't explicitly state what at least in my area of study seems to have been the critical factor: wheels weren't useful in much of this territory.

Arab traders engaged in trans-Saharan trade were perfectly aware that wheels existed, but they were utterly useless given the terrain that they were traversing. Instead they relied on enormous camel trains to transport their goods.

The most technologically advanced solution is not always the most economical. Richard Bulliett, who has written a lot on these questions including I think a history of the wheel which unfortunately I have not read, has commented on how in contemporary Pakistan there are regions where transport by camel is still the most economically wise investment, not over just any wheeled vehicles but over mechanized trucks.