The bioaccessibility of zinc (Zn), calcium (Ca), magnesium (Mg), and selenium (Se) from various nuts (Brazil nuts, walnuts, peanuts, almonds, cashews, pecans, hazelnuts, macadamia nuts, and pistachios) was assessed using a simulated two-phase model of enzymatic digestion in vitro. The levels of Zn, Mg, and Ca were determined by atomic absorption spectrometry, and Se was measured by inductively coupled plasma-mass spectrometry. All tested nuts were good sources of Mg, and most, except macadamia nuts, were also good sources of Zn (the standard portion covers over 15% of NRV–R (UE) 1924/2006). Brazil nuts had the highest Se content. Almonds and Brazil nuts were rich in Ca. Se demonstrated the highest bioaccessibility from nuts (27.7% to 70.65%), whereas Ca exhibited the lowest bioaccessibility (below 9%). Pistachios had the highest Zn bioavailability, while cashews excelled in Mg bioaccessibility. Macadamia and pistachios were top for Ca bioaccessibility, and Brazil nuts for Se. Bioaccessibility is positively correlated with fat (for Zn: r = 0.23), carbohydrates (for Mg: 0.44; for Ca: 0.35), and sugar content (for Zn: r = 0.36; for Mg: 0.46; for Ca: 0.40).