  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 d\phi/dE \propto E^{-Gamma}, with a
Crab-like photon spectral index of Gamma=2.6. The upper limit above 200 GeV is
6.4\times10^{-12} cm^{-2}s^{-1} and above 1 TeV is 7.4\times10^{-13}
cm^{-2}s^{-1}. We obtained an upper limit for the pulsed emission of
2.6\times10^{-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.
