Abstract The interplanetary magnetic field carried out from the Sun by the solar wind displays fluctuations over a wide range of scales. While at large scales, say at frequencies lower than 0.1–1 Hz, fluctuations display the universal character of fully developed turbulence with a well-defined Kolmogorov-like inertial range, the physical and dynamical properties of the small-scale regime as well as their connection with the large-scale ones are still a debated topic. In this work we investigate the near-Sun magnetic field fluctuations at subproton scales by analyzing the Markov property of fluctuations and recovering basic information about the nature of the energy transfer across different scales. By evaluating the Kramers–Moyal coefficients we find that fluctuations in the subproton range are well described as a Markovian process with Probability Density Functions (PDFs) modeled via a Fokker–Planck (FP) equation. Furthermore, we show that the shape of the PDFs is globally scale-invariant and similar to the one recovered for the stationary solution of the FP equation at different scales. The relevance of our results on the Markovian character of subproton scale fluctuations is also discussed in connection with the occurrence of turbulence in this domain.