KM3NeT is a research infrastructure being installed in the deep Mediterranean Sea. It will house a neutrino telescope comprising hundreds of networked moorings - detection units or strings - equipped with optical instrumentation to detect the Cherenkov radiation generated by charged particles from neutrino-induced collisions in its vicinity. In comparison to moorings typically used for oceanography, several key features of the KM3NeT string are different: the instrumentation is contained in transparent and thus unprotected glass spheres; two thin Dyneema (R) ropes are used as strength members; and a thin delicate backbone tube with fibre-optics and copper wires for data and power transmission, respectively, runs along the full length of the mooring. Also, compared to other neutrino telescopes such as ANTARES in the Mediterranean Sea and GVD in Lake Baikal, the KM3NeT strings are more slender to minimise the amount of material used for support of the optical sensors. Moreover, the rate of deploying a large number of strings in a period of a few years is unprecedented. For all these reasons, for the installation of the KM3NeT strings, a custom-made, fast deployment method was designed. Despite the length of several hundreds of metres, the slim design of the string allows it to be compacted into a small, re-usable spherical launching vehicle instead of deploying the mooring weight down from a surface vessel. After being lowered to the seafloor, the string unfurls to its full length with the buoyant launching vehicle rolling along the two ropes. The design of the vehicle, the loading with a string, and its underwater self-unrolling are detailed in this paper.