Summary: Let \(G\) be a locally compact Abelian group and \(A\) a commutative semisimple Banach algebra with a minimal approximate identity. The isometric multipliers of \(L^1(G,A)\) onto itself are shown to be of the form \(F\delta_t\) where \(F\) is an isometric multiplier of \(A\) onto \(A\) and \(t\in G\). A similar result for \(L^p(G,A)\), \(1< p<\infty\), \(p\neq 2\), is also established under certain conditions.