Borrowed from a language of Northern Italy (cf. Venetan valís, Lombard valiza), from Medieval Latin valesia, valixia, from Late Latin valisia, possibly from Gaulish *valisia (“leather bag”), from Proto-Celtic *wal- (“to enclose, surround”), from Proto-Indo-European *welH-. Or, possibly from Arabic وَلِيهَة (walīha, “large bag”).
Related to French valise and Spanish valija, though it is unclear if either term was borrowed from the other.