The pressure dependence of electronic structure, exchange interactions, and Curie temperature in the ferromagnetic Heusler alloy Ni₂MnSn has been studied theoretically within the framework of the density-functional theory. The calculation of the exchange parameters is based on the frozen-magnon approach. The Curie temperature T_c is calculated within the mean-field approximation by solving the matrix equation for a multi-sublattice system. In agreement with the experiment the Curie temperature increased from 362 K at ambient pressure to 396 K at 12GPa. Extending the variation of the lattice parameter beyond the range studied experimentally, we obtained nonmonotonic pressure dependence of the Curie temperature and metamagnetic transition. We relate the theoretical dependence of T_c on the lattice constant to the corresponding dependence predicted by the empirical interaction curve. The Mn-Ni atomic interchange observed experimentally is simulated to study its influence on the Curie temperature.