Summary: We obtain the Singleton bound for poset block codes and define a maximum distance separable poset block code (MDS \((P, \pi)\)-code) as a code meeting this bound. We extend the concept of \(I\)-balls to poset block metric and describe \(r\)-perfect and MDS \((P, \pi)\)-codes in terms of \(I\)-perfect codes. As a special case when all the blocks have the same dimension, we establish that MDS \((P, \pi)\)-codes are same as \(I\)-perfect codes for \(I \in \mathcal{I}^{\frac{ n - k}{ m}}(P)\). We show that the duality result also holds for this case. Further, we determine the weight enumerator of an MDS \((P, \pi)\)-code.