We present the first results from very-high-energy observations of the dwarf spheroidal satellite candidate Triangulum II with the MAGIC telescopes from 62.4 hours of good-quality data taken between August 2016 and August 2017. We find no gamma-ray excess in the direction of Triangulum II, and upper limits on both the differential and integral gamma-ray flux are presented. Currently, the kinematics of Triangulum II are affected by large uncertainties leading to a bias in the determination of the properties of its dark matter halo. Using a scaling relation between the annihilation J-factor and heliocentric distance of well-known dwarf spheroidal galaxies, we estimate an annihilation J-factor for Triangulum II for WIMP dark matter of $log[J_{text{ann}}({0.5^{circ}})/$ GeV$^{2}$ cm$^{-5}] = 19.35 pm 0.37$. We also derive a dark matter density profile for the object relying on results from resolved simulations of Milky Way sized dark matter halos. We obtain 95% confidence-level limits on the thermally averaged annihilation cross section for WIMP annihilation into various Standard Model channels. The most stringent limits are obtained in the $tau^{+}tau^{-}$ final state, where a cross section for annihilation down to $langle sigma_{text{ann}} v rangle = 3.05 times 10^{-24}$ cm$^{3}$ s$^{-1}$ is excluded.
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