We compute the fragmentation functions for the production of a Higgs boson at $$ \mathcal{O} $$ O ($$ {y}_t^2 $$ y t 2 αs). As part of this calculation, the relevant splitting functions are also derived at the same perturbative order. Our results can be used to compute differential cross sections with arbitrary top-quark and Higgs-boson masses from massless calculations. They can also be used to resum logarithms of the form ln(pT/m) at large transverse momentum pT to next-to-leading-logarithmic accuracy by solving the DGLAP equations.