Packaging containing nanoparticles (NPs) can increase the shelf life of products, but the presence of NPs may hazards human life. In this regard, there are reports regarding the side effect and cytotoxicity of nanoparticles. The main aim of this research was to study the migration of silver and copper nanoparticles from the packaging to the food matrix as well as the assessment techniques. The diffusion and migration of nanoparticles can be analyzed by analytical techniques including atomic absorption, inductively coupled plasma mass spectrometry, inductively coupled plasma atomic emission, and inductively coupled plasma optical emission spectroscopy, as well as X-ray diffraction, spectroscopy, migration, and titration. Inductively coupled plasma-based techniques demonstrated the best results. Reports indicated that studies on the migration of Ag/Cu nanoparticles do not agree with each other, but almost all studies agree that the migration of these nanoparticles is higher in acidic environments. There are widespread ambiguities about the mechanism of nanoparticle toxicity, so understanding these nanoparticles and their toxic effects are essential. Nanomaterials that enter the body in a variety of ways can be distributed throughout the body and damage human cells by altering mitochondrial function, producing reactive oxygen, and increasing membrane permeability, leading to toxic effects and chronic disease. Therefore, more research needs to be done on the development of food packaging coatings with consideration given to the main parameters affecting nanoparticles migration.