Topologically ordered states of matter are generically characterized by excitations with quantum number fractionalization. A prime example is the spin liquid realized in Kitaev's honeycomb-lattice compass model where spin-flip excitations fractionalize into Majorana fermions and Ising gauge fluxes. While numerous compounds have been proposed to be proximate to such a spin-liquid phase, clear-cut evidence for fractionalized excitations is lacking. Here we employ microwave absorption measurements to study the low-energy excitations in α-RuCl3 over a wide range of frequencies, magnetic fields, and temperatures, covering in particular the vicinity of the field-driven quantum phase transition where long-range magnetic order disappears. In addition to conventional gapped magnon modes we find a highly unusual broad continuum characteristic of fractionalization which - most remarkably - extends to energies below the lowest sharp mode and to temperatures significantly higher than the ordering temperature and develops a gap of a nontrivial origin in strong magnetic fields. Our results unravel the signatures of fractionalized excitations in α-RuCl3 and pave the way to a more complete understanding of the Kitaev spin liquid and its instabilities.