Processes with identified hadrons require the introduction of fragmentation functions to describe the hadronisation of a quark or a gluon into the observed hadron particle. Such identified particles in the final state make the treatment of infrared divergences more subtle, because of additional collinear divergences to be handled. We extend the antenna subtraction method to include hadron fragmentation processes up to next-to-next-to-leading order (NNLO) in QCD in $e^+e^-$ collisions. To this end, we introduce new double-real and real-virtual fragmentation antenna functions in the final-final kinematics, with associated phase space mappings. These antenna functions are integrated over the relevant phase spaces, retaining their dependence on the momentum fraction of the fragmenting parton.