  We present the first branon dark matter (DM) search in the very high-energy
gamma-ray band with observations of the dwarf spheroidal galaxy Segue~1 carried
out by the Major Atmospheric Gamma Imaging Cherenkov (MAGIC) telescope system.
Branons are new degrees of freedom that appear in flexible brane-world models
corresponding to brane fluctuations. They behave as weakly interacting massive
particles, which are natural DM candidates. In the absence of a gamma-ray
signal in the Segue~1 data, we place constraints on the branon DM parameter
space by using a binned likelihood analysis. Our most constraining limit to the
thermally-averaged annihilation cross-section (at $95\%$ confidence level)
corresponds to $ \langle \sigma v \rangle \simeq 1.4 \times
10^{-23}~\text{cm}^{3}\text{s}^{-1} $ at a branon DM mass of $ \sim
0.7~\text{TeV}$.
