Context. It has been claimed that the nova-like cataclysmic variable AE Aquarii (AE Aqr) is a very-high-energy (VHE, E> 100 GeV) source both on observational and theoretical grounds. Aims: We search for VHE γ-ray emission from AE Aqr during different states of the source at several wavelengths to confirm or rule out previous claims of detection of γ-ray emission from this object. Methods: We report on observations of AE Aqr performed by MAGIC. The source was observed during 12 h as part of a multiwavelength campaign carried out between May and June 2012 covering the optical, X-ray, and γ-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. Results: AE Aqr was not detected at VHEs 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 dφ/ dE ∝ E- Γ, with a Crab-like photon spectral index of Γ = 2.6. The upper limit above 200 GeV is 6.4 × 10-12 cm-2 s-1 and above 1 TeV is 7.4 × 10-13 cm-2 s-1. We obtained an upper limit for the pulsed emission of 2.6 × 10-12 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. Conclusions: Our results indicate that AE Aqr is not a VHE γ-ray emitter at the level of emission previously claimed. We have established the most constraining upper limits for the VHE γ-ray emission of AE Aqr.