North Africa including Egypt was Roman.
The Periplus Maris Erythraei was written in Greek in the first century CE. It meticulously describes ports, people, and navigation of the Red Sea, the Arab coast, the way to India, and the coast of East Africa. Roman trade went as far south as modern Kenya, Tanzania, and possibly northern Mozambique.
For West Africa, there's a Greek translation of the periplus by Hanno the Navigator, a Carthaginian explorer of the 5th century BCE.
Africa may have been mapped and explored by the Phoenicians. Herodotus in his histories includes an intriguing tidbit about the Phoenician sailors who circumnavigated Africa (then called "Libya"):
Libya is washed on all sides by the sea except where it joins Asia, as was first demonstrated, so far as our knowledge goes, by the Egyptian king Necho, who, after calling off the construction of the canal between the Nile and the Arabian Gulf, sent out a fleet manned by a Phoenician crew with orders to sail west about and return to Egypt and the Mediterranean by way of the Straits of Gibraltar. The Phoenicians sailed from the Arabian Gulf into the southern ocean, and every autumn put in at some convenient spot on the Libyan coast, sowed a patch of ground, and waited for next year's harvest. Then, having got in their grain, they put to sea again, and after two full years rounded the Pillars of Heracles in the course of the third, and returned to Egypt. These men made a statement which I do not myself believe, though others may, to the effect that as they sailed on a westerly course round the southern end of Libya, they had the sun on their right - to northward of them. This is how Libya was first discovered by sea.
While this is the only account of the voyage, the thing that makes it more likely is exactly the fact that Herodotus was skeptical of: that the sun (at its zenith) was in the northern part of the sky, which only happens in the southern hemisphere. But because Herodotus did not know the earth was round (or at least did not consider the implications of that fact), he thought the sailors were telling a tall tale.
To put this story in a timeframe, Necho II was the ruler of the kingdom along the Nile from 610 to 595 BCE, so this is a little before the age of classical Greece.