  We report the results of the observation of the nearby satellite galaxy Segue
1 performed by the MAGIC-I ground-based gamma-ray telescope between November
2008 and March 2009 for a total of 43.2 hours. No significant gamma-ray
emission was found above the background. Differential upper limits on the
gamma-ray flux are derived assuming various power-law slopes for the possible
emission spectrum. Integral upper limits are also calculated for several
power-law spectra and for different energy thresholds. The values are of the
order of 10^{-11} ph cm^{-2}$ s^{-1} above 100 GeV and 10^{-12} ph cm^{-2}
s^{-1} above 200 GeV. Segue 1 is currently considered one of the most
interesting targets for indirect dark matter searches. In these terms, the
upper limits have been also interpreted in the context of annihilating dark
matter particles. For such purpose, we performed a grid scan over a reasonable
portion of the parameter space for the minimal SuperGravity model and computed
the flux upper limit for each point separately, taking fully into account the
peculiar spectral features of each model. We found that in order to match the
experimental upper limits with the model predictions, a minimum flux boost of
10^{3} is required, and that the upper limits are quite dependent on the shape
of the gamma-ray energy spectrum predicted by each specific model. Finally we
compared the upper limits with the predictions of some dark matter models able
to explain the PAMELA rise in the positron ratio, finding that Segue 1 data are
in tension with the dark matter explanation of the PAMELA spectrum in the case
of a dark matter candidate annihilating into tau+tau-. A complete exclusion
however is not possible due to the uncertainties in the Segue 1 astrophysical
factor.
