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 \sim 0.9 keV ) and a power-law component ( \Gamma \sim 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 \sim 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 . Conclusions :