We report the parameter-free, density functional theory calculations of interatomic exchange interactions and Curie temperatures of half-metallic ferrimagnetic full Heusler alloys Mn₂VZ (Z=Al,Ge). To calculate the interatomic exchange interactions we employ the frozen magnon approach. The Curie temperatures are calculated within the mean-field approximation to the classical Heisenberg Hamiltonian by solving a matrix equation for a multi-sublattice system. Our calculations show that, although a large magnetic moment is carried by Mn atoms, competing ferromagnetic (inter-sublattice) and antiferromagnetic (intra-sublattice) Mn-Mn interactions in Mn₂VAl almost cancel each other in the mean-filed experienced by the Mn atoms. In Mn₂VGe the leading Mn-Mn exchange interaction is antiferromagnetic. In both compounds the ferromagnetism of the Mn subsystem is favoured by strong antiferromagnetic Mn-V interactions. The obtained value of the Curie temperature of Mn₂VAl is in good agreement with experiment. For Mn₂VGe there is no experimental information available and our calculation is a prediction.