Context. High energy particles reside in the relativistic jets of microquasars, making them possible sources of very high energy radiation (VHE, $>$100 GeV). Detecting this emission would provide a new handle on jet physics. Aims. Observations of the microquasar GRS 1915+105 with the HESS telescope array were undertaken in 2004–2008 to search for VHE emission. Methods. Stereoscopic imaging of Cherenkov radiation from extensive air showers is used to reconstruct the energy and direction of the incident gamma rays. Results. There is no evidence for a VHE gamma-ray signal either from the direction of the microquasar or its vicinity. An upper limit of $6.1\times 10^{-13}$ ph cm$^{-2}$ s$^{-1}$ (99.9% confidence level) is set on the photon flux above 410 GeV, equivalent to a VHE luminosity of ${∼} 10^{34}$ erg s$^{-1}$ at 11 kpc. Conclusions. The VHE to X-ray luminosity ratio in GRS 1915+105 is at least four orders of magnitude lower than the ratio observed in gamma-ray binaries. The VHE radiative efficiency of the compact jet is less than 0.01% based on its estimated total power of 10$^{38}$ erg s$^{-1}$. Particle acceleration in GRS 1915+105 is not efficient at high energies and/or the magnetic field is too strong. It is also possible that VHE gamma-rays are produced by GRS 1915+105, but the emission is highly time-dependent.