  The high-frequency-peaked BL Lac (HBL) 1ES 0806+524 (z = 0.138) was
discovered in VHE $\gamma$ rays in 2008. Until now, the broad-band spectrum of
1ES 0806+524 has been only poorly characterized, in particular at high
energies. We analysed multiwavelength observations from $\gamma$ rays to radio
performed from 2011 January to March, which were triggered by the high activity
detected at optical frequencies. These observations constitute the most precise
determination of the broad-band emission of 1ES 0806+524 to date. The
stereoscopic MAGIC observations yielded a $\gamma$-ray signal above 250 GeV of
$(3.7 \pm 0.7)$ per cent of the Crab Nebula flux with a statistical
significance of 9.9 $\sigma$. The multiwavelength observations showed
significant variability in essentially all energy bands, including a VHE
$\gamma$-ray flare that lasted less than one night, which provided
unprecedented evidence for short-term variability in 1ES 0806+524. The spectrum
of this flare is well described by a power law with a photon index of $2.97 \pm
0.29$ between $\sim$150 GeV and 1 TeV and an integral flux of $(9.3 \pm 1.9)$
per cent of the Crab Nebula flux above 250 GeV. The spectrum during the
non-flaring VHE activity is compatible with the only available VHE observation
performed in 2008 with VERITAS when the source was in a low optical state. The
broad-band spectral energy distribution can be described with a one-zone
Synchrotron Self Compton model with parameters typical for HBLs, indicating
that 1ES 0806+524 is not substantially different from the HBLs previously
detected.
