In this paper, the well-known Hulthen potential is used for describing the plasma screening effect on a hydrogen atom embedded in weakly coupled plasma. As the radial Schrdinger equation with Hulthen potential gives analytical solutions, the energy levels and wave functions are obtained in a closed form. Structural properties such as dipole polarizability, transition probability, and oscillator strength are calculated easily using the corresponding analytical formulas. Moreover, the analytic solutions of the Hulthen potential enable us to obtain many other observables reliably. Asymptotic iteration method solutions of the Hulthen potential for different screening parameters are considered to calculate the transition energies, oscillator strength, and transition probability values for a few dipole allowed states of hydrogen atom embedded in weakly coupled plasma. Use of the Hulthen potential to determine the screening effects on hydrogen atom embedded in weakly coupled plasma would be useful for modeling Debye plasma in investigations of the atomic structure and collisions in the plasma physics field.