We consider the Kaluza-Klein scenario in which gravity propagates in the $4+n$ dimensional bulk of spacetime and the Standard Model particles are confined to a 3-brane. We calculate the gauge boson self-energy corrections arising from the exchange of virtual gravitons and present our results in the $STU$-formalism. We find that the new physics contributions to $S$, $T$ and $U$ decouple in the limit that the string scale $M_S$ goes to infinity. The oblique parameters constrain the lower limit on $M_S$. Taking the quantum gravity cutoff to be $M_S$, $S$-parameter constraints impose $M_S>1.55$ TeV for $n=2$ at the 1$��$ level. $T$-parameter constraints impose $M_S>1.25 (0.75)$ TeV for $n=3 (6)$.

Version to appear in PRD