The effect of the plasma environment on the structure and properties of Na I and K I atoms is studied using the Fock-space multireference coupled-cluster theory in the relativistic framework. The Debye-Hückle model is used to account the effect of the plasma environment on the atoms. A significant change in the ionization energies, transition energies, transition probabilities, and oscillator strengths of Na I and K I atoms is seen when they are immersed in plasma. The number of bound states and the binding energies of plasma embedded Na I and K I reduce notably in comparison to the isolated plasma free atoms, and these changes tend the system towards gradual instability. The transition spectra of Na I and K I show red shifts in the presence of plasma screening, whereas the oscillator strengths show the red and blue shifts for the same and different principal quantum number transitions, respectively. Furthermore, the presence of plasma screening causes the suppression of spontaneous transition probabilities of plasma embedded Na I and K I atoms. These results are useful to interpret the spectral lines of astrophysical plasma and to get insights into the physical processes that are operative in the celestial objects.