In Greek mythology, there were two people named Icarius (/ᵻˈkɛəriəs/; Ancient Greek: Ἰκάριος Ikários).
One Icarius was the son of either Perieres and Gorgophone or of Oebalus and Bateia, brother of Hippocoon and Tyndareus and, through Periboea, father of Penelope, Perileos, Thoas, Damasippus, Imeusimus, Aletes and Iphthime. According to other traditions, he was the father of Penelope, Alyzeus and Leucadius by Polycaste. His other possible wives were Dorodoche (daughter of Ortilochus) and Asterodia (daughter of Eurypylus); the latter was said to have born him five sons - Amasichus, Phalereus, Thoon, Pheremmelias, Perilaos - and a daughter Laodice or Laodamia. He was a Spartan king and a champion runner who would not allow anyone to marry his daughter unless he beat him in a race. Odysseus succeeded and married Penelope. After they got married, Icarius tried to persuade Odysseus to remain in Sparta. He did leave with Penelope, but Icarius followed them, imploring his daughter to stay. Odysseus told her she must choose whether to be with her father or with her husband. Penelope did not answer, but modestly covered her face with a veil. Icarius correctly understood that this was a sign of her will to leave with Odysseus, let them go and erected a statue of Aidos (Modesty) on the spot. Icarius was apparently still alive at the time of the events of the Odyssey.