Classical Greek and Latin poetry did not usually rhyme, but rhyme was used very occasionally. For instance, Catullus includes partial rhymes in the poem Cui dono lepidum novum libellum. The ancient Greeks knew rhyme, and rhymes in The Wasps by Aristophanes are noted by a translator.
Rhyme is central to classical Arabic poetry tracing back to its 6th century pre-Islamic roots. According to some archaic sources, Irish literature introduced the rhyme to Early Medieval Europe, but that is a disputed claim. In the 7th century, the Irish had brought the art of rhyming verses to a high pitch of perfection. The leonine verse is notable for introducing rhyme into High Medieval literature in the 12th century.
Rhyme entered European poetry in the High Middle Ages, in part under the influence of the Arabic language in Al Andalus (modern Spain). Arabic language poets used rhyme extensively from the first development of literary Arabic in the sixth century, as in their long, rhyming qasidas.
Source: Rhyme – Wikipedia