Magnetic nanoparticles such as FePt in the L10-phase are the bedrock of our current data storage technology. As the grains become smaller to keep up with technological demands, the superparamagnetic limit calls for materials with higher magneto-crystalline anisotropy. This in turn reduces the magnetic exchange length to just a few nanometers enabling magnetic structures to be induced within the nanoparticles. Here we describe the existence of spin-wave solitons, dynamic localized bound states of spin-wave excitations, in FePt nanoparticles. We show with time-resolved X-ray diffraction and micromagnetic modeling that spin-wave solitons of sub-10 nm sizes form out of the demagnetized state following femtosecond laser excitation. The measured soliton spin-precession frequency of 0.1 THz positions this system as a platform to develop miniature devices capable of filling the THz gap.