  In this paper we investigate spherically symmetric vacuum solutions of $f(R)$
gravity in a higher dimensional spacetime. With this objective we construct a
system of non-linear differential equations, whose solutions depend on the
explicit form assumed for the function $F(R)=\frac{df(R)}{dR}$. We explicit
show that for specific classes of this function exact solutions from the field
equations are obtained; also we find approximated results for the metric tensor
for more general cases admitting $F(R)$ close to the unity.
