Indications of a GeV component in the emission from gamma-ray bursts (GRBs) are known since the Energetic Gamma-Ray Experiment Telescope observations during the 1990s and they have been confirmed by the data of the Fermi satellite. These results have, however, shown that our understanding of GRB physics is still unsatisfactory. The new generation of Cherenkov observatories and in particular the MAGIC telescope, allow for the first time the possibility to extend the measurement of GRBs from several tens up to hundreds of GeV energy range. Both leptonic and hadronic processes have been suggested to explain the possible GeV/TeV counterpart of GRBs. Observations with ground-based telescopes of very high energy (VHE) photons (E > 30 GeV) from these sources are going to play a key role in discriminating among the different proposed emission mechanisms, which are barely distinguishable at lower energies. MAGIC telescope observations of the GRB 090102 (z = 1.547) field and Fermi Large Area Telescope data in the same time interval are analysed to derive upper limits of the GeV/TeV emission. We compare these results to the expected emissions evaluated for different processes in the framework of a relativistic blastwave model for the afterglow. Simultaneous upper limits with Fermi and a Cherenkov telescope have been derived for this GRB observation. The results we obtained are compatible with the expected emission although the difficulties in predicting the HE and VHE emission for the afterglow of this event makes it difficult to draw firmer conclusions. Nonetheless, MAGIC sensitivity in the energy range of overlap with space-based instruments (above about 40 GeV) is about one order of magnitude better with respect to Fermi. This makes evident the constraining power of ground-based observations and shows that the MAGIC telescope has reached the required performance to make possible GRB multiwavelength studies in the VHE range.