Several low-power kiloparsec-scale jets in nearby radio galaxies are known for their synchrotron radiation extending up to optical and X-ray photon energies. Here we comment on high-energy gamma-ray emission of one particular object of this kind, i.e., the kiloparsec-scale jet of the M87 radio galaxy, resulting from Comptonization of the starlight photon field of the host galaxy by the synchrotron-emitting jet electrons. In our analysis, we include the relativistic bulk velocity of the jet, as well as the Klein-Nishina effects. We show that upper limits to the kiloparsec-scale jet inverse Compton radiation imposed by the HESS and HEGRA Cerenkov Telescopes-which detected a variable source of very high energy gamma-ray emission within 0 degrees.1 (similar to 30 kpc) of the M87 central region-give us an important constraint on the magnetic field strength in this object, namely, that the magnetic field cannot be smaller than the equipartition value ( referring solely to the radiating electrons) in the brightest knot of the jet, and most likely, is even stronger. In this context, we point out a need for the amplification of the magnetic energy flux along the M87 jet from the subparsec to kiloparsec scales, suggesting the turbulent dynamo as a plausible process responsible for the aforementioned amplification.