The similarity between the two is that both systems suppose that physical objects exist because of (Plato) Ideal Forms or those objects have meaning because of (structuralism) underlying structures.
Plato believed that material objects (people, trees, chairs, etc,) are rough approximations of Ideal Forms existing in a realm of perfection. For example, a carpenter doesn't build a chair based on sensory perception of other chairs he's seen. Rather, he builds the chair based on a mental understanding of the function of a chair, of the Ideal Form of the chair. The physical chair works if it accurately depicts the Ideal chair. However, a material chair can never be as perfect as the abstract Ideal chair. Plato believed that the realm of Ideal Forms (structures) was true reality. So, the physical chair is not the true chair. It is a less perfect, physical representation of that Ideal chair.
Saussure was arguably the first influential theorist of Structuralism. Saussure described the component of language as the sign, made up of a signifier and a signified. For example, the signifier (the word) "chair" is a representation of the signified thing - chair.
In structuralism, we do not understand what a chair is because it is called a "chair." If we were speaking German, we would say "stuhl." The connection between the signifier "chair" and the thing chair is arbitrary. What gives the chair meaning is its relation to other things within a system. For example, I know "chair" if I know other things such as chairs are used for sitting. "Chair" or "economy" have meaning based on how they function within a system of other words and signified meanings. With Plato, "chair" has meaning based upon an Ideal Form.
Saussure described the abstract, systematic rules of language (la langue) as different from language enacted in daily life (parole). Similar to the structure of la langue, other structuralists hold that there is a realm of culture, a "third order" comprised of a structure that is distinct from the physical world and the imagination. This "third order" is similar to Plato's realm of Ideal Forms in being separate from reality, but there are differences. Plato's Ideal Realm is perfect, immortal, and the true reality. The structuralist "third order" is a part of culture and although it is abstract, it comes from interactions in real life; not some Ideal plain of perfection. If these structures underlie all meaning in human activity, they can hardly be perfect.
Therefore, an abstract structural design of capitalism arises, not from some Ideal Form of economics, but from the actual economic interactions (and ideologies) of capitalist practice in the physical world.
So, there are some similarities of these two actually very different philosophies separated by nearly 2000 years. The difference is that in Plato's thinking, things in the physical world reflect more perfect, Ideal forms. In structuralism, things in the physical world have meaning because of how they relate to each other within a structural framework, a set of rules derived from mental and physical interaction.