Let $R$ be a ring. A right $R$-module $M$ is called minimal
quasi-injective if every homomorphism from a simple submodule of
$M$ to $M$ can be extended to an endomorphism of $M$. Some
characterizations and properties of minimal quasi-injective
modules are given. Some results of Nicholson and Yousif on
mininjective rings are extended to these modules. Besides, V-rings
are characterized by minimal quasi-injective modules.