How is linear momentum conserved in case of a freely falling body?

Linear Momentum is conserved only in systems with net external force equal to zero. For a body falling on Earth, it experiences Earth's gravitational force so its linear Momentum increases. But if you include Earth in your system then definitely, momentum is conserved, as an equal amount of momentum of Earth is increased in upward direction. But individually for both it's not conserved, there is an external force of gravity on each.

Linear momentum of a system remains conserved unless an external force acts on it. Since during free fall, a gravitational force acts on the body, it's momentum will not remain conserved. However, if we change the reference in such a manner that the gravitational force becomes an internal force of the system, i.e. regard both the body and Earth together as a system, and consider this system to be isolated in the universe, with no other body present near the system, we can now apply the law of conservation of linear momentum as there are no external forces acting on the system now.

Sciencisco's is the best, but I thought I would add one thought: the external potential $V = mgy$ does not exhibit translational symmetry in the $y$ direction. Noether's theorem says that each symmetry gives a conservation law. Furthermore, if you don't have a symmetry, then you don't have the associated conservation law. Translational symmetry gives us conservation of momentum. Because this potential is not translationally invariant in the $y$ direction, momentum is not conserved in that direction.