Since the domain of $y=f(\log_{2}x)$ is $\left[\frac{1}{2}, 4\right]$,
it follows that $\frac{1}{2} \leq x \leq 4$.
Then $-1 \leq \log_{2}x \leq 2$.
Thus, the domain of $y=f(x)$ is $[-1, 2]$.
Therefore, the correct choice is: $\boxed{\text{C}}$.
From the domain of $y=f(\log_{2}x)$ being $\left[\frac{1}{2}, 4\right]$, we can deduce that $\frac{1}{2} \leq x \leq 4$, and further determine the domain of $y=f(x)$.
This question examines the domain of a function and its determination method, and is a basic question.