A set of B(E2) values for the low-lying excited states in the radioactive isotope Sn-109 were deduced from a Coulomb excitation experiment. The 2.87-MeV/u radioactive beam was produced at the REX-ISOLDE facility at CERN and was incident on a secondary Ni-58 target. The B(E2) values were determined using the known 2(+) -> 0(+) reduced transition probability in Ni-58 as normalization with the semiclassical Coulomb excitation code GOSIA2. The transition probabilities are compared to shell-model calculations based on a realistic nucleon-nucleon interaction and the predictions of a simple core-excitation model. This measurement represents the first determination of multiple B(E2) values in a light Sn nucleus using the Coulomb excitation technique with low-energy radioactive beams. The results provide constraints for the single-neutron states relative to Sn-100 and also indicate the importance of both single-neutron and collective excitations in the light Sn isotopes.