The invention relates to a tool (1) and a method for the automatic remote application of strips of non-adhesive fibre-reinforced polymer (FRP) tape (12) for the covering of curved or flat surfaces (20) of construction elements, such as tunnel vaults, parabolic arches, catenary arches and other non-funicular arches typical of bridges and many modern constructions. The tool includes a frame having the following elements coupled thereto, namely: a pressure roller (2); a means for dispensing FRP tape via guide rollers (6a, 6b, 6c, 6d); a drive roller (5); and a means for dispensing adhesive so as to coat said tape, such that by moving the tool over the surface, power is generated and transmitted to an FRP-tape-dispensing means, adjusted such that the FRP dispensing speed is substantially similar to the tool (1) movement speed, thus allowing an automatic remote application method.