In 1977 L. Solomon introduced certain zeta functions in the study of lattices over orders in semisimple algebras over \({\mathbb{Q}}\). Implicit in Solomon's original definitions was the parallel concept of a zeta function associated with lattices over orders in semisimple \({\mathbb{F}}_ q(X)\)-algebras, where \({\mathbb{F}}_ q(X)\) is the field of rational functions over the finite field \({\mathbb{F}}_ q.\) The author defines the Solomon zeta function over such function fields, and derives some of their properties. For instance, he extends to the present case the proof by Solomon, Bushnell and Reiner of some conjectures made by Solomon in the rational case.