In Greek mythology, Epaphus (Ancient Greek: Ἔπαφος, romanized: Épaphos), also called Apis or Munantius, was a son of Zeus and Io and a king of Egypt. His name is associated with "touch," referring to Zeus conceiving him by the touch of his hand. By Memphis (or Cassiopeia) he was father of Libya, and through her an ancestor of Belus and Agenor.

Epaphus's mother was Io; he was thus brother of Ceroessa. With his wife Memphis (or, according to others, Cassiopeia) he had a daughter Libya; some accounts add another daughter, Lysianassa. These daughters later became mothers of Poseidon's sons — Belus, Agenor, and possibly Lelex by the former, Busiris by the latter. Through these daughters Epaphus was the ancestor of the "dark Libyans, and high-souled Aethiopians, and the Underground-folk and feeble Pygmies."

In one account, Epaphus had a son, Dorus, who fathered Pygmaeus, ancestor of the Pygmies. Otherwise, this tribe of diminutive men was instead born from Epaphus and Gaea (Earth).

The name Epaphus means "Touch," referring to the manner in which he was conceived, by the touch of Zeus's hand. He was born in Euboea, in the cave Boösaule according to Strabo, or according to others in Egypt on the river Nile after the long wanderings of his mother. He was then concealed by the Curetes at Hera's request, but Io sought and afterward found him in Syria, where he was nursed by the wife of the king of Byblus.

Epaphus was also a contemporary and rival of Phaethon, son of Helios and Clymene. He criticized Phaethon's parentage, prompting Phaethon to undertake his fateful journey in his father's chariot of the sun.

Epaphus is regarded in the myths as the founder of Memphis in Egypt. Hera, envious that her husband's bastard ruled such a great kingdom, saw to it that Epaphus should be killed while hunting.