Aims: We obtained phase-resolved spectroscopy of the accreting millisecond X-ray pulsar SAX J1808.4-3658 during its outburst in 2008 to find a signature of the donor star, constrain its radial velocity semi-amplitude (K_2), and derive estimates for the pulsar mass. Methods: Using Doppler images of the Bowen region, we find a significant (≥8σ) compact spot at a position where the donor star is expected. If this is a signature of the donor star, we measure K_em = 248±20 km s-1 (1σ confidence), which represents a strict lower limit to K_2. Also, the Doppler map of He II λ4686 shows the characteristic signature of the accretion disc, and there is a hint of enhanced emission that may be a result of tidal distortions in the accretion disc that are expected in very low mass-ratio interacting binaries. Results: The lower limit on K2 leads to a lower limit on the mass function of f(M_1) ≥ 0.10 M_&sun;. Applying the maximum K-correction gives 228 < K2 < 322 km s-1 and a mass ratio of 0.051 < q < 0.072. Conclusions: Despite the limited S/N of the data, we were able to detect a signature of the donor star in SAX J1808.4-3658, although future observations during a new outburst are still needed to confirm this. If the derived K_em is correct, the largest uncertainty in determining of the mass of the neutron star in SAX J1808.4-3658 using dynamical studies lies with the poorly known inclination. Based on observations made with ESO Telescopes at the Paranal Observatory under programme ID 281.D-5060(A).