In this paper we consider Iwahori Whittaker functions on n-fold metaplectic covers ˜G of G(F) with G a split reductive group over a non-archimedean local field F. For every element ϕ of a basis of Iwahori Whittaker functions, and for every g∈˜G, we evaluate ϕ(g) by recurrence relations over the Weyl group using "vector Demazure-Whittaker operators." Specializing to the case of G=GLr, we exhibit a solvable lattice model whose partition function equals ϕ(g). These models are of a new type associated with the quantum affine super group Uq(^gl(r|n)). The recurrence relations on the representation theory side then correspond to solutions to Yang-Baxter equations for the lattice models.