We present a first-principles study of the electronic structure and exchange interactions in Si/Mn digital magnetic alloy (DMA) consisting of Mn monolayers embedded in a Si matrix stacking along [001] direction. The main focus of our study is on the dependence of magnetic properties on the morphology of the Mn monolayer. Three different structural models for the Mn monolayer are considered: manganese in substitutional (i), interstitial (ii), and both interstitial and substitutional (iii) positions. The atomic positions in Si/Mn DMA are determined by means of the VASP code and then serve as input for multiple-scattering calculations for the electronic and magnetic structure. The magnetic force theorem is used to evaluate the exchange coupling parameters. A Heisenberg model based on those parameters is used to estimate magnon frequencies and magnetic phase-transition temperatures for different anisotropies. The magnetic properties of Si/Mn DMA are found to be strongly dependent on the underlying crystalline structure.