We report on the detection of X-ray pulsations at 2.1 ms from the known X-ray burster IGR J17379-3747 using XMM-Newton. The coherent signal shows a clear Doppler modulation from which we estimate an orbital period of ~1.9 hours and a projected semi-major axis of ~8 lt-ms. Taking into account the lack of eclipses (inclination angle of < 75 deg) and assuming a neutron star mass of 1.4 Msun, we estimated a minimum companion star of ~0.06 Msun. Considerations on the probability distribution of the binary inclination angle make less likely the hypothesis of a main-sequence companion star. On the other hand, the close correspondence with the orbital parameters of the accreting millisecond pulsar SAX J1808.4-3658 suggests the presence of a bloated brown dwarf. The energy spectrum of the source is well described by a soft disk black-body component (kT ~0.45 keV) plus a Comptonisation spectrum with photon index ~1.9. No sign of emission lines or reflection components is significantly detected. Finally, combining the source ephemerides estimated from the observed outbursts, we obtained a first constraint on the long-term orbital evolution of the order of dP_orb/dt = (-2.5 +/- 2.3)E-12 s/s.