Context.A new accreting millisecond X-ray pulsar, IGR J17511−3057, was discovered in outburst on 2009 September 12 during the INTEGRAL Galactic bulge monitoring programme. Aims. To study the evolution of the source X-ray flux and spectral properties during the outburst, we requested a Swift monitoring of IGR J17511−3057. Methods. In this paper we report on the results of the first two weeks of monitoring the source. Results. The persistent emission of IGR J17511−3057 during the outburst is modelled well with an absorbed blackbody (kT ∼ 0.9 keV) and a power-law component (Γ∼ 1-2), similar to what has been observed from other previously known millisecond pulsars. Swift also detected three type-I Xray bursts from this source. By assuming that the peak luminosity of these bursts is equal to the Eddington value for a pure helium type-I X-ray burst, we derived an upper limit to the source distance of ∼10 kpc. The theoretically expected recurrence time of the bursts according to the helium burst hypothesis is 0.2-0.9 days, in agreement with the observations.