I'm pretty sure that the hands are held on by pressure only. Some watches have a dress cap on the end of the canon pinion(the stem that the minutehand in attached to - I'm pretty sure that's what's it called), but that doesn't 'hold' the hand onto the stem. The hand could have been taken off wrong or too many times and, now, the hole in it has been enlarged.
You could try very carefully and ever so slightly to squeeze the holes' shaft(whatever that would be called

) with tweezers to make it smaller then press the hand back on. You may need a new hand all together and in the least hopefully the cannon pinion isn't damaged.
Good luck.