The exchange took place in a part of the Jufra region controlled by Field Marshal Khalifa Haftar, near a ceasefire line between eastern and western forces.
According to the reports and images on social media, pilot Amer al-Orfi al-Gajam was exchanged for 15 prisoners held by Haftar's forces, which back a rival government and control much of eastern and southern Libya.
Images on social media appeared to show Gajam, a high-ranking member of Haftar's forces, with a long beard and dressed in a traditional Libyan tunic and vest.
The 2011 revolt that toppled Moamar Kadhafi's regime left a power vacuum that was filled by an array of armed groups.
Haftar's east-based forces, the self-styled Libyan National Army, were among the most powerful groups that emerged in the aftermath.
In 2019, Haftar seized large parts of the south and launched an assault on Tripoli.
In December that year, government forces said they had shot down a Russian-made MiG-23 fighter jet some 45 kilometres (28 miles) west of the capital, capturing its pilot Gajam.
Haftar's forces later announced that they had lost a MiG-23 due to a "technical fault" and that the pilot had been captured.
They made no immediate statement on the reported prisoner exchange.