A method and an apparatus for closing a tubular knitted article at one of its axial ends, at the end of its production cycle on a circular knitting machine for hosiery or the like. The method consists in ending the production of an article at one of its axial ends. The article is then picked up from the machine and transferred to a handling device located in a sewing or looping station. The pick-up is performed by transferring individually the loops of the last row of knitting from the needles of the machine to spikes of the handling device, which has an annular body composed of two semiannular elements. The article is then turned, and one of the two semiannular elements is turned over with respect to the other one, so that the spikes of one semiannular element face, and are aligned with, the spikes of the other semiannular element. The loops of knitting arranged on the spikes of one semiannular element are transferred to the spikes of the other semiannular element so that each spike of the latter semiannular element supports a pair of loops of knitting.