At face-value, this is demonstrably possible. A video game is a simulation of a world. Some video-games have mini games inside them, a simulation inside a simulation. A movie, in some sense, is a simulation of a world, and many movies contain other movies inside them. I assume these examples wouldn't qualify in your view, but that raises the question "what counts as a simulation?" for your purposes.
I'm going to assume you mean something that could convincingly replace the world as we experience it. (Let's avoid the entire question of consciousness by assuming a brain-in-a-vat setup. The brain is conscious, but all its sensory data is generated by a computer.) Could a simulation of that caliber contain another simulation of that caliber wholly inside itself, where the child simulation must be built entirely from entities of the parent simulation (we can't cheat and just simulate both worlds at the root level)? In principle, there doesn't seem to be anything that would prevent this in terms of overall mechanics. Just as an emulation of any computer can be built on any other computer, it should be possible to build one simulation inside another.
However, your question specifically calls out the question of size. Can a universe of the same size/complexity as the parent universe be built inside of it? Intuitively, the answer is no, the child universe would need to be smaller (simpler). However, there are ways around this. There's an old stage trick where the painted backdrop makes the actors look as if they are in the wide-open outdoors, when in fact they are in a small enclosed room. Similarly, many video games use a "skybox" to make the in-game universe seem big and expansive, even though only a portion of it has actually been constructed. Any given person has personally experienced only an infinitesimal portion of our seemingly infinite universe. If it were simulated, it's possible it could be far smaller than we think.