Strong-field physics, an extreme limit of light–matter interaction1,2,3, is expanding into the realm of surfaces4,5and nanostructures6,7,8,9,10,11from its origin in atomic and molecular science12,13,14,15. The attraction of nanostructures lies in two intimately connected features: local intensity enhancement and sub-wavelength confinement of optical fields. Local intensity enhancement facilitates access to the strong-field regime and has already sparked various applications, whereas spatial localization has the potential to generate strong-field dynamics exclusive to nanostructures. However, the observation of features unattainable in gaseous media is challenged by many-body effects and material damage, which arise under intense illumination of dense systems16,17,18,19. Here, we non-destructively access this regime in the solid state by employing single plasmonic nanotips and few-cycle mid-infrared pulses, making use of the wavelength-dependence of the interaction, that is, the ponderomotive energy. We investigate strong-field photoelectron emission and acceleration from single nanostructures over a broad spectral range, and find kinetic energies of hundreds of electronvolts. We observe the transition to a new regime in strong-field dynamics, in which the electrons escape the nanolocalized field within a fraction of an optical half-cycle. The transition into this regime, characterized by a spatial adiabaticity parameter, would require relativistic electrons in the absence of nanostructures. These results establish new degrees of freedom for the manipulation and control of electron dynamics on femtosecond and attosecond timescales, combining optical near-fields and nanoscopic sources.