Author’s abstract: In this paper, we study modules having the property that are invariant under some idempotent endomorphisms of its injective envelope. Such modules are called essentially \(\pi \)-injective. It is shown that (1) \(M\) is essentially \(\pi \)-injective iff for any essentially finite direct summand \(X_1\) of \(M\) and any submodule \(X_2\) of \(M\) with \(X_1\cap X_2=0\), there exists a direct summand \(X_0\) of \(M\) containing \(X_2\) such that \(M= X_1\oplus X_0\), (2) \(M\) is essentially \(\pi \)-injective iff \(M\) is an ef-extending right \(R\)-module and for any decomposition \(M= M_1\oplus M_2\) with \(M_1\) essentially finite, \(M_1\) and \(M_2\) are relatively injective, (3) if \(M\) is essentially \(\pi \)-injective and \(R\) satisfies ACC on right ideals of the form \(r(m)\), \(m\in M \), then \(M\) is a direct sum of uniform submodules. We also describe rings via essentially \(\pi \)-injective modules. It is shown that \(R\) is a semisimple artinian ring iff the direct sum of any two essentially \(\pi \)-injective right \(R\)-modules is essentially \(\pi \)-injective.