We have observed cyclotron resonance in the layered perovskite superconductor Sr2RuO4. We obtain cyclotron masses for the alpha, beta, and gamma Fermi surfaces of (4.33+/-0.05)m(e), (5.81+/-0. 05)m(e), and (9.71+/-0.2)m(e), respectively. The appreciable differences between these results and those obtained from de Haas-van Alphen measurements are attributable to strong electron-electron interactions in this system. Our findings appear to be consistent with predictions for an interacting Fermi liquid; indeed, semiquantitative agreement is obtained for the electron pockets beta and gamma.