This paper investigates the concept of annihilator essential injectivity in the setting of R-modules, where R is unital ring. An R-module M2 is termed annihilator essentially M1-injective if every R-homomorphism from A ≤ M1 to  M2 with an annihilator essential kernel can be extended to M1. We prove that this injective property is closed under taking submodules and factor modules of M1, as well as direct products. By providing illustrative examples, we demonstrate the distinction between annihilator essential injectivity and other classical forms of injectivity. These findings provide new insights into the study of relative injectivity and the classification of modules.