A search for the indirect effects of the gravitational interaction in extra dimensions on the process e+e->e+e- is presented. Data from the OPAL experiment at LEP at centre-of-mass energies between 183 GeV and 209 GeV are compared with the predictions of models including quantum gravity in extra dimensions. The data are found to be onsistent with the Standard Model, and 95% confidence level lower limits on the scale M_s>1.00 TeV for lambda = +1 and M_s >1.15 TeV for lambda = -1 are derived. These results are combined with limits derived from mu-mu, tau-tau, gamma-gamma and ZZ final states at OPAL. The combined 95% confidence level lower limits are M_s>1.03 TeV for lambda = +1 and M_s>1.17 TeV for lambda = -1.