The electronic structure and magnetic properties of Mn₁-xCrxSb alloys were investigated for the full concentration range. The stability of the concentration-dependent magnetic structure of the alloys were analysed on the basis of spin-spiral calculations as well as using the Monte Carlo (MC) simulations based on the Heisenberg model with the exchange coupling parameters calculated from first-principles. A leading contribution to the canted magnetic structure in Mn₁-xCrxSb is the competition of the direct Cr-Cr and Mn-Mn exchange interactions having opposite signs. Furthermore, a strong impact of long-distance RKKY-type interactions is demonstrated. MC simulations at finite temperature were used to obtain the magnetic phase diagram for Mn₁-xCrxSb alloys, which is in reasonable agreement with the experimental data.