We present Ulysses and NEAR data from the detection of the short or intermediate duration (2 s) gamma-ray burst GRB 000301C (2000 March 1.41 UT). The gamma-ray burst (GRB) was localised by the Inter Planetary Network (IPN) and RXTE to an area of ~50 arcmin 2. A fading optical counterpart was subsequently discovered with the Nordic Optical Telescope (NOT) about 42 h after the burst. The GRB lies at the border between the long-soft and the short-hard classes of GRBs. If GRB 000301C belongs to the latter class, this would be the first detection of an afterglow to a short-hard burst. We present UBRI photometry from the time of the discovery until 11 days after the burst. We also present JHK photometry obtained with UKIRT on 2000 March 4.5 UT (3.1 days after the burst). Finally, we present spectroscopic observations of the optical afterglow obtained with the ESO VLT Antu telescope 4 and 5 days after the burst. The optical light curve is consistent with being achromatic from 2 to 11 days after the burst and exhibits a break. A broken power-law fit yields a shallow pre-break decay power-law slope of $\alpha_1=-0.72 \pm 0.06$, a break time of $t_{\rm break}=4.39 \pm 0.26$ days after the burst, and a post-break slope of $\alpha_2=-2.29 \pm 0.17$. These properties of the light curve are best explained by a sideways expanding jet in an ambient medium of constant mean density. In the optical spectrum we find absorption features that are consistent with Fe ii, C iv, C ii, Si ii and Ly α at a redshift of $2.0404 \pm 0.0008$. We find evidence for a curved shape of the spectral energy distribution of the observed afterglow. It is best fitted with a power-law spectral distribution with index $\beta\sim -0.7$ reddened by an SMC-like extinction law with $A_{\rm V}\sim 0.1$ mag. Based on the Ly α absorption line we estimate the H i column density to be $\log$( N(H i) $)=21.2 \pm 0.5$. This is the first direct indication of a connection between GRB host galaxies and Damped Ly α Absorbers.
