The tablet was discovered after three years of surface excavations by the Greek Archaeological Services in cooperation with the German Institute of Archaeology.
It was found close to the remains of the Temple of Zeus at the cradle of the Olympic Games in western Peloponnese.
The plaque is "a great archaeological, epigraphic, literary and historical exhibit," the ministry said.
First composed orally around the 8th century BC, the epic — which is attributed to ancient Greek author Homer — was later transcribed during the Christian era onto parchment of which only a few fragments have been discovered in Egypt. It was probably handed down in oral tradition for hundreds of years before first being written down.
The Odyssey is a Greek poem that tells of the return journey of Odysseus to the island of Ithaca after the war at Troy. The war lasted 10 years and Odysseus spent an additional 10 years trying to get home in the face of difficulties from Poseidon, god of the earth and sea.
The section that has been found is part of The Odyssey's 14th Rhapsody in which Odysseus talks to his friend Eumaeus, the first mortal he meets after returning to Ithaca.