The present invention relates to a therapeutic sleeve made of knitted fabric with graduated compression that has multifunctional characteristics and that favours conditions for preventing the appearance or worsening of lymphoedema in limbs, avoiding swelling in limbs, and increasing the wearers thermophysiological, ergonomic and psychological comfort during use.This sleeve or therapeutic device, produced by small-diameter double cylinder knitting machines, contains structural modifications that enable several levels of compression to be obtained in the same tube of knitted fabric, with greater compression in the wrist region and less compression in the shoulder region.The variation in compression, together with the type of fibrous materials used and the sleeve design, as well as the possibility of attaching it to a piece of clothing, help maximise the wearers thermophysiological and psychological comfort during use.