We report on the fabrication of cellulose nanofibers from Fique (Furcraea andina), in which raw macrofibers were chemically treated and then ground. Bleaching was effective in removing lignin from the raw fibers, and this was confirmed with distinct techniques, viz. X-ray diffraction, FTIR spectroscopy, thermogravimetric analysis, and the estimation of the kappa number. From scanning electron microscopy and transmission electron microscopy images, the nanofibers were seen to form a network with 85% of nanofibers having diameters smaller than 50 nm, while their length was hundreds of nanometers. The tensile strength of membranes made with the nanofibers was 166 MPa. These membranes had no cytotoxicity in in vitro indirect tests analyzed qualitatively and quantitatively. Indeed, cell viability was higher for the nanofibers than the negative control.