We classify the indecomposable injective E(n)⁎E(n)-comodules, where E(n) is the Johnson-Wilson homology theory. They are suspensions of the $J_{n,r}=E\left(n\right)⁎\left(M_{r}E\left(r\right)\right)$, where 0 ≤ r ≤ n, with the endomorphism ring of $J_{n,r}$ being $\widehat{E\left(r\right)}*\widehat{E\left(r\right)}$, where $\widehat{E\left(r\right)}$ denotes the completion of E(r).