It has been claimed that the nova-like cataclysmic variable (CV) AE Aquarii (AE Aqr) is a very-high-energy (VHE, $E>$100 GeV) source both on observational and theoretical grounds. We aim to search for VHE gamma-ray emission from AE Aqr during different states of the source at several wavelengths to confirm or rule out previous claims of detection of gamma-ray emission from this object. We report on observations of AE Aqr performed by MAGIC. The source was observed during 12 hours as part of a multiwavelength campaign carried out between May and June 2012 covering the optical, X-ray, and gamma-ray ranges. Besides MAGIC, the other facilities involved were the KVA, Skinakas, and Vidojevica telescopes in the optical and Swift in X-rays. We calculated integral upper limits coincident with different states of the source in the optical. We computed upper limits to the pulsed emission limiting the signal region to 30% of the phaseogram and we also searched for pulsed emission at different frequencies applying the Rayleigh test. AE Aqr was not detected at VHE energies during the multiwavelength campaign. We establish integral upper limits at the 95% confidence level for the steady emission assuming the differential flux proportional to a power-law function dphi/dE propto E^{-Gamma}, with a Crab-like photon spectral index of Gamma=2.6. The upper limit above 200 GeV is 6.4times10^{-12} cm^{-2}s^{-1} and above 1 TeV is 7.4times10^{-13} cm^{-2}s^{-1}. We obtained an upper limit for the pulsed emission of 2.6times10^{-12} cm^{-2}s^{-1} for energies above 200 GeV. Applying the Rayleigh test for pulsed emission at different frequencies we did not find any significant signal. Our results indicate that AE Aqr is not a VHE gamma-ray emitter at the level of emission previously claimed. We have established the most constraining upper limits for the VHE gamma-ray emission of AE Aqr.
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