Nuts used as a snack and meal accompaniment supply plant protein and fatty acids that are beneficial for human health; however, they can also provide minerals. The aim of this study was to determine the content of selected elements that are often deficient in the diet (calcium, potassium, magnesium, selenium, and zinc) in nuts and determine whether they can be used to supplement deficiencies in the diet. In this study, we analyzed 10 types of nuts (n = 120 samples) that are consumed and available for sale in Poland. The content of calcium, magnesium, selenium, and zinc was determined by the atomic absorption spectrometry method, and flame atomic emission spectrometry was used for determination of potassium contents. The highest median calcium content was found in almonds (2825.8 mg/kg), the highest potassium content in pistachio nuts (15,730.5 mg/kg), the highest magnesium and selenium contents in Brazil nuts (10,509.2 mg/kg and 4348.7 μg/kg, respectively), and the highest zinc content in pine nuts (72.4 mg/kg). All the tested nuts are a source of magnesium, eight types of tested nuts are a source of potassium, six nut types are a source of zinc, and four nut types are a source of selenium; however, among the tested nuts, only almonds can be considered a source of calcium. Moreover, we found that selected chemometric methods can be useful in the classification of nuts. The studied nuts are valuable products that can be used to supplement the diet with selected minerals and can therefore be labelled as functional products crucial for disease prevention.