We investigate spectral properties of turbulence in the solar wind that is a weakly collisional astrophysical plasma, accessible to in-situ observations. Using the Helios search coil magnetometer measurements in the fast solar wind, in the inner heliosphere, we focus on properties of the turbulent magnetic fluctuations at scales smaller than the ion characteristic scales, the so-called kinetic plasma turbulence. At such small scales, we show that the magnetic power spectra between 0.3 and 0.9 AU from the Sun have a generic shape ∼ f −8/3 exp (−f /f d) where the dissipation frequency f d is correlated with the Doppler shifted frequency fρe of the electron Larmor radius. This behavior is statistically significant: all the observed kinetic spectra are well described by this model, with f d = fρe/1.8. Our results indicate that the electron gyroradius plays the role of the dissipation scale and marks the end of the electromagnetic cascade in the solar wind.