The Player's Handbook mentions that high intelligence is very important for a thief, but Intelligence Table I does not list a minimum value for a thief, only for an assassin.
Is there a minimum value?
No, there's no minimum Int value for a thief. The lack of other mechanics in AD&D1 leaves a lot that is later moved to proficiencies (and in 3.x, skills) to simple attribute checks, and so one could reasonably expect a 1E DM to call for lots of Int Rolls to do various theifly things, like case a joint, spot the watch, etc.
Despite all that, no minimum was ever required to be a Thief; the sole requirement was (and even in later editions, still is) Dex 9+, and only Dex.
6 is the minimum for all classes except the fighter, which can have 3-5 as well. The Thief needs a 9 or better in dexterity & 6 or better in all other attributes, save for wisdom, which can be as low as 3.