As someone who does this a living - there is no minimum sample size. It all depends on your (desired) label claim for Sensitivity and Specificity, the significance and power desired, whether or not your test will use different types of samples (whole blood, plasma, serum, tissue, fecal, urine etc.) and the need for diversity of disease variants (such as geographic stratification).
It will also depend on the type of analysis your regulatory reviewer prefers...latent class, baysian, clopper-pearson...