We have studied magnetic interactions in zinc-blende MnAs as a function of volume by ab initio density-functional calculations. The calculated Heisenberg pair-exchange parameters show a strong volume dependence. The calculated Curie temperatures, obtained by Monte Carlo simulations using ab initio parameters and a classical Heisenberg Hamiltonian, show a decreasing trend upon compression. Analysis of cross sections of Fermi surfaces indicate a nesting feature for compressed volumes, which can give rise to competing exchange interactions. Calculations of self-consistent noncollinear spin configurations indicate that spins deviate strongly from collinear ordering for low volumes whereas they align in a collinear ferromagnetic fashion for high volumes. Also, for expanded volumes, the calculated Curie temperature is around 600 K signifying the possibility of using MnAs for future room-temperature spintronic applications.