We investigate the possibility of erosion of planetesimals in a protoplanetary disk. We use theory and direct numerical simulations (lattice Boltzmann method) to calculate the erosion of large-much larger than the mean-free path of gas molecules-bodies of different shapes in flows. We find that erosion follows a universal power law in time, at intermediate times, independent of the Reynolds number of the flow and the initial shape of the body. Consequently, we estimate that planetesimals in eccentric orbits, of even very small eccentricity, rapidly (in about 100 yr) erodes away if the semimajor axis of their orbit lies in the inner disk-less than about 10 au. Even planetesimals in circular orbits erode away in approximately 10,000 yr if the semimajor axis of their orbits are <0.6 au.