We prove that Thompson's group F(n) is not minimally almost convex with respect to the standard finite generating set. A group G with Cayley graph Γ is not minimally almost convex if for arbitrarily large values of m there exist elements g,h∈ B_m such that d_Γ(g,h)=2 and d_Bm(g,h)=2m. (Here B_m is the ball of radius m centered at the identity.) We use tree-pair diagrams to represent elements of F(n) and then use Fordham's metric to calculate geodesic length of elements of F(n). Cleary and Taback have shown that F(2) is not almost convex and Belk and Bux have shown that F(2) is not minimally almost convex; we generalize these results to show that F(n) is not minimally almost convex for all n∈{2,3,4,...}.