The device (10) comprises a container (11), closed by a lid (14), for holding the lubricating fluid; a strip of felt or the like is immersed in the container and becomes impregnated with the fluid by capillary action. One end of the strip protrudes from the lid of the container (11) and wraps around a cylindrical support so that a respective portion (13a) of the strip (13), shaped like a cylindrical sector and impregnated with lubricating fluid, protrudes with respect to the surface of the lid (14) and is exposed. The weft thread (F) to be lubricated is made to slide on the exposed portion (13a) of the strip, and means (18-19-20-21) are provided for guiding the thread and for producing a cyclic transverse movement thereof from one end to the other of the exposed portion (13a).