As military prizes, medals have been awarded, as far as I know, since roman times. Ever since the time of Lucius Tarquinius Priscus, soldiers or officers who distinguished themselves in battle would get an ornate metal disk called phalera. The soldiers or officers would wear them on the armour for parades, triumphs, and such. In the ordinary course of affairs, they did not wear them, but the phalerae were placed on the soldier's legion's standard.
Source: Goldsworthy, Adrian, The complete Roman army, Thames and Hudson, 2003, pages 96 and 97.