Aims. The aim of this study is to search for evidence of a common emission engine between radio giant pulses (GPs) and very-high-energy (VHE, E > 100 GeV) γ-rays from the Crab pulsar. Methods. We performed 16 h of simultaneous observations of the Crab pulsar at 1.4 GHz with the Effelsberg radio telescope and the Westerbork Synthesis Radio Telescope (WSRT), and at energies above 60 GeV we used the Major Atmospheric Gamma-ray Imaging Cherenkov (MAGIC) telescopes. We searched for a statistical correlation between the radio and VHE γ-ray emission with search windows of different lengths and different time lags to the arrival times of a radio GP. A dedicated search for an enhancement in the number of VHE γ-rays correlated with the occurrence of radio GPs was carried out separately for the P1 and P2 phase ranges, respectively. Results. In the radio data sample, 99444 radio GPs were detected. We find no significant correlation between the GPs and VHE photons in any of the search windows. Depending on phase cuts and the chosen search windows, we find upper limits at a 95% confidence level on an increase in VHE γ-ray events correlated with radio GPs between 7% and 61% of the average Crab pulsar VHE flux for the P1 and P2 phase ranges, respectively. This puts upper limits on the flux increase during a radio GP between 12% and 2900% of the pulsed VHE flux, depending on the search window duration and phase cuts. This is the most stringent upper limit on a correlation between γ-ray emission and radio GPs reported so far.